Title and Abstract of Talks：
PDF




JostHinrich Eschenburg 
Title:
Submanifolds and Bott Periodicity (Joint work with Bernhard Hanke) 

Abstract:
Some compact symmetric spaces have poles and equators
like spheres. Poles are points with the same geodesic
symmetry, and equators contain the midpoints of shortest
geodesics between poles. These are reflective submanifolds
called centrioles. Some centrioles have topological
meaning as homotopy approximations of the full path space,
thus iterated centrioles serve to compute higher homotopy
groups. This is the basic idea of Milnor's version of
Bott's periodicity theorem. We want to show that this
idea can be applied also to the vector bundle versions
of the periodicity theorem. As an example, we will talk
about a new proof for the theorem of Atiyah, Bott, and
Shapiro (1964) which relates vector bundles over spheres
to Clifford modules; these in turn are related to
iterated centrioles of the classical groups.
(Common work with Bernhard Hanke, Augsburg)


Title:
What is a Penrose tiling? (Special Talk) 

Abstract:
As finite beings with only a finite set of ideas in mind,
how can we invent tilings covering the whole infinite plane
(complete tilings)? In art, two answers have been
developed: Periodicity (a finite domain repeats itself
in two directions) and Self Similarity (a small area
determines the pattern for a larger area). In 1974,
Roger Penrose introduced a class of tilings which
are not periodic but have a certain self similarity
property. They are constructed from two types of tiles,
based on the geometry of the regular pentagon. So far
there is no valid constuctive definition for Penrose
tilings which are extendible to complete ones. Matching
rules (see Wikipedia article on Penrose tilings) are
not sufficient as we will see. One way to construct
complete tilings is by projecting a strip of a higher
dimensional regular grid. However, we will give an
example of a Penrose tiling which does not arise in
this way. We use an extremely narrow definition of
Penrose tilings which seems to completely determine
those patterns, but still it allows uncountably many
different patterns, including all projection tilings.
This finding was heavily influenced by some 400 years
old Islamic patterns at Isfahan, Iran.
(Common work with H.J. Rivertz, Trondheim, Norway)


Marcos Alexandrino (1) 
Title: Mean curvature flow of orbits of isometric actions 

Abstract:
Given a proper isometric action on a compact manifold, we study the mean curvature flow equation
with a principal orbit of this action as initial datum.
We prove that any finite time singularity is a singular orbit, and the singularity is of type I.
These results are proved in the more general context of Singular Riemannian foliations and
generalize previous results of Liu and Terng, Pacini and Koike.
This talk is based on a joint work with Dr. Marco Radeschi (wwu Munster) and
is aimed at a broad audience of students, faculties and researchers.
M.M. Alexandrino and M. Radeschi, Mean curvature flow of singular Riemannian foliations,
to appear in The Journal of Geometric Analysis (2015) see also arXiv:1408.543


Marcos Alexandrino (2) 
Title: Isometry flows on orbit spaces 

Abstract:
In this talk, we discuss the following result:
Given a proper isometric action $K\times M\to M$ on a complete Riemannian manifold $M$
then each continuous isometric flow on the orbit space $M/K$ is smooth,
i.e., it is the projection of an $K$equivariant smooth flow on the manifold $M$.
The first application of our result concerns Molino's conjecture,
which states that the partition of a Riemannian manifold into the closures of the leaves of
a singular Riemannian foliation is still a singular Riemannian foliation.
We prove Molino's conjecture for the main class of foliations considered in his book,
namely orbitlike foliations. We also discuss smoothness of isometric actions on orbit spaces.
This talk is based on a joint work with Dr. Marco Radeschi (wwu Munster)
and is aimed at a broad audience of students, faculties and researchers in Geometry.
ps: I will also briefly explain current works and how this talk is related to holonomy foliation
that is associated to every connections on fiber bundles.


Leonardo Biliotti（University of Parma, Italy)

Title: Stability of measures on Kähler manifolds 

Abstract:
Let M be a Kähler manifold and let K be a compact group that acts on M
in a Hamiltonian fashion. We will study the action of K and its
complexification G on the space of probability measures on M.
First of all we identify an abstract setting for the momentum mapping
and give numerical criteria for stability, semistability and polystability.
Next we apply this setting to the action of G on measures. We get various
stability criteria for measures on Kähler manifolds. The same circle of
ideas gives a very general surjectivity result for a map originaly
studied by Hersch and BourguignonLiYau. This is a joint work with
Dott. Alessandro Ghigi.


Juergen Berndt（King's College London, UK) 
Title: Compact homogeneous Riemannian manifolds with low coindex of symmetry 
Abstract:
The coindex of symmetry measures in how far a homogeneous Riemannian manifold deviates
from being a Riemannian symmetric space.
In the talk we will discuss some general structure theory for compact homogeneous Riemannian manifolds
in relation to the coindex of symmetry. We also present a classification of compact homogeneous
Riemannian manifolds with coindex of symmetry less or equal than three.
This is joint work with Carlos Olmos (Cordoba) and Silvio Reggiani (Rosario),
to appear in Journal of the European Mathematical Society (see also arXiv:1312.6097).


Young Jin Suh（Kyungpook National University, Korea) 
Title: Recent progress on complex quadrics in Hermitian Symmetric Spaces


Abstract:
In this talk we will give some background on the geometry of complex quadric
$Q^m=SO(m+2)/SO(2)xSO(m)$ which can be regarded as Hermitian Symmetric Space with rank 2 of compact type.
We will give some detailed explanations about the progress on real hypersurfaces in the complex quadric
$Q^m$ for Ricci parallel, harmonic curvature, normal Jacobi operator, pseudoEinstein real hypersurfaces,
and pseudoanti commuting and Ricci soliton problem etc.


Jong Ryul Kim（Kunsan National University) 
Title:
A gradient Ricci soliton with a regular hypersurface
of a potential function $f$ and $\text{Hess}f(\nabla f, \nabla f)=0$


Abstract:
For a complete oriented Riemannian manifold $M$ of a gradient Ricci soliton
with a regular level hypersurface $H_s=\{x\in Mf(x)=s\}$
for a potential function $f$ with a unit normal vector field $N=\frac{\nabla f}{\nabla f}$ on $H_s$,
we show that if $\text{Ric}(N,N)=\lambda$ and $D_{E_i} R =2\text{Ric}(\nabla f,E_i)$ is constant
for a local geodesic frame $\{E_i\}_{i=1}^{n1}$ of $(\nabla f)^\perp$,
then $M$ is Ricci flat and each level hypersurface is totally geodesic.
Moreover $M$ is a product manifold $H_s\times \mathbb {R}$.


Hiroyuki Tasaki（University of Tsukuba) 
Title:
Maximal antipodal sets of oriented real Grassmann manifolds


Abstract:
An antipodal set in a compact Riemannian symmetric space is a subset where
the restriction of the symmetry at each point is the identity, which was
introduced by Chen and Nagano. A maximal antipodal set is a kind of frame
of a compact Riemannian symmetric space. In this talk I mainly treat
maximal antipodal sets of oriented real Grassmann manifolds. We can reduce
the classification of these to a combinatorial problem and classify these
in the case where the rank is less than five. Moreover we can estimate the
cardinalities of maximal antipodal sets in cases of higher rank.


Makiko Sumi Tanaka（Tokyo University of Science) 
Title:
Antipodal sets of compact Riemannian symmetric spaces


Abstract:
A subset of a compact Riemannian symmetric space is called an antipodal
set if the geodesic symmetry at each point is the identity on the set. The
cardinalities of antipodal sets are finite. An antipodal set whose
cardinality attains the maximum of the cardinalities of antipodal sets is
called a great antipodal set. In a symmetric Rspace, a maximal antipodal
set is a great antipodal set and a great antipodal set is unique up to the
action of the identity component of the isometry group, moreover, a great
antipodal set is an orbit of the Weyl group. On the other hand, we have
not known much about antipodal sets of a compact Riemannian symmetric
space which is not a symmetric Rspace. In this talk we will present a
classification of maximal antipodal subgroups in a quotient group of a
compact Lie group of classical type and that in G_2. In many of these
cases there exists a maximal antipodal subgroup but not a great antipodal
subgroup. This talk is based on joint work with Hiroyuki Tasaki. 

Takashi Sakai (Tokyo Metropolitan University) 
Title:
Biharmonic homogeneous submanifolds in compact symmetric spaces


Abstract:
In 1983, J. Eells and L. Lemaire extended the notion of harmonic map between
Riemannian manifolds to that of biharmonic map, which is defined as a critical point
of the bienergy functional. G.Y. Jiang studied the first and second variation formulas
of the bienergy functional and obtained the EulerLagrange equation, which is a fourth
order PDE. In this talk, first we study biharmonic submanifolds in Einstein manifolds,
and give a necessary and sufficient condition for a submanifold whose tension field is
parallel to be biharmonic. For orbits of commutative Hermann actions in compact symmetric
spaces, this condition can be described in terms of symmetric triads. By using this
criterion, we construct some proper biharmonic submanifolds in compact symmetric spaces,
which are orbits of commutative Hermann actions. Here, proper biharmonic means that
biharmonic, but not harmonic.
This talk is based on a joint work with Shinji Ohno and Hajime Urakawa.


Naoyuki Koike（Tokyo University of Science) 
Title:
Volumepreserving mean curvature flow for tubes in symmetric spaces


Abstract:
In this talk, we first state the evolutions of the radius function and its gradient along the volumepreserving
mean curvature flow starting from a tube (of nonconstant radius) over a compact closed domain of a reflective
submanifold in a symmetric space under certain condition for the radius function.
Next, we prove that the tubeness is preserved along the flow in the case where the ambient space is a rank one
symmetric space of compact type (other than a sphere), the reflective submanifold is an invariant submanifold and
the initial radius function is radial.
Furthermore, in this case, we prove that the flow exists in infinite time or reaches to
one of the invariant submanifold, a focal submanifold of the invariant submanifold and the cut locus of
the intersection point in a normal umbrella of the invariant submanifold.


Hiroshi Tamaru（Hiroshima University) 
Title:
Realizations of some contact metric manifolds as Ricci soliton real
hypersurfaces


Abstract:
Ricci soliton contact metric manifolds with some nullity conditions
have recently been studied by Ghosh and Sharma.
Whereas the gradient case is wellunderstood,
they provided a list of candidates for the nongradient case.
These candidates can be realized as Lie groups,
but one only knows the bracket relations of the Lie algebras,
which are hard to be understood apart from the threedimensional case.
In this talk,
we will study these spaces with higherdimensions,
and prove that the simplyconnected ones can be realized as
homogeneous real hypersurfaces in noncompact twoplane Grassmannians.
These realizations enable us to prove, in a Lietheoretic way,
that all of them are actually Ricci solitons.
This talk is based on a joint work with
Jong Taek Cho, Takahiro Hashinaga, Akira Kubo, and Yuichiro Taketomi.


Takayuki Okuda (Hiroshima University) 
Title:
Pairs of conjugacy classes of reflective submanifolds of Riemmanian symmetric spaces with discrete intersections


Abstract:
Let M = G/K be a Riemannian symmetric space of compact or noncompact type.
In this talk, we classify pairs of reflective submanifolds L_1 and L_2
in M such that the intersection of L_1 and gL_2 is discrete in M for any g in G.
We will also talk about relations between such pairs (L_1,L_2) and
discontinuous groups for certain pseudoRiemmanian symmeric spaces.


Hyunjin Lee and Young Jin Suh (Kyungpook National University, Korea)

Title:
Some parallel Hopf hypersurfaces in complex hyperbolic twoplane Grassmannians


Abstract:
In this talk, we first consider a concept named the cyclic parallelism for the shape operator
of a real hypersurface~$M$ in complex hyperbolic twoplane Grassmannian.
Moreover, we prove that the cyclic parallelism is to be a Reeb parallelism on $M$.
Hence, we study the Reeb parallelism by the LeviCivita and generalized TanakaWebster connections on $M$.
Related to these notions, we give some characterizations of Hopf hypersurfaces
in complex hyperbolic twoplane Grassmannians. 

Eunmi Pak and Young Jin Suh (Kyungpook National University, Korea)

Title:
Results on Jacobi operators of real hypersurfaces in complex twoplane Grassmannians


Abstract:
In relation to the generalized TanakaWebster connection,
we consider a new notion of parallel Jacobi operator for real hypersurfaces in
complex twoplane Grassmannians and show results about real hypersurfaces in
complex twoplane Grassmannians with generalized TanakaWebster
parallel structure Jacobi operator and normal Jacobi operator.


Changhwa Woo, Hyunjin Lee and Young Jin Suh (Kyungpook National University, Korea)

Title:
Real hypersurfaces in complex hyperbolic twoplane Grassmannians
with commuting restricted structure Jacobi operators


Abstract:
In this paper, we introduce a new commuting condition between
the structure Jacobi operator and symmetric (1,1)type tensor field $T$,
that is, $R_{\xi}\phi T=TR_{\xi}\phi$, where $T=A$ or $T=S$ for Hopf hypersurfaces
in complex hyperbolic twoplane Grassmannians. By using simultaneous diagonalzation
for commuting symmetric operators, we give a complete classification of real hypersurfaces
in complex hyperbolic twoplane Grassmannians with commuting condition respectively.


Doo Hyun Hwang and Young Jin Suh (Kyungpook National University, Korea) 
Title:
Hopf hypersurfaces in complex two plane Grassmannians satisfying recurrent Ricci tensors


Abstract:
In this paper, we have introduced a new notion of generalized Tanaka–Webster Reeb recurrent Ricci tensor
of real hypersurfaces in complex twoplane Grassmannians. Next, we show a nonexistence property
for real hypersurfaces $M$
in complex twoplane Grassmannians with such a curvature condition.


Gyu Jong Kim and Young Jin Suh (Kyungpook National University, Korea)

Title:
Real hypersurfaces in complex twoplane Grassmannians with Killing structure Jacobi operator


Abstract:
In this talk, we introduce a notion of the complex twoplane Grassmannians and a geometric meaning of
Killing structure Jacobi operator. Then we give a nonexistence theorem for a real hypersurface
in complex twoplane Grassmannians satisfies the condition of Killing structure Jacobi operator.


Shinji Ohno (Tokyo Metropolitan University)

Title:
A construction of weakly reflective submanifolds in compact symmetric spaces


Abstract:
A submanifold of a Riemannian manifold is called a weakly reflective submanifold
if for any point in the submanifold and each normal vector at the point,
there exists a weakly reflection which is an isometry on the ambient Riemannian manifold.
The notion of weakly reflective submanifold is a generalization of the notion of reflective
submanifold. Reflective submanifolds in irreducible compact symmetric spaces are classified.
In contrast, examples of weakly reflective submanifolds in compact symmetric spaces are not
well known except for examples in hyperspheres. In this talk we will give examples of weakly
reflective submanifolds in compact symmetric spaces as orbits of Hermann actions
which are generalizations of isotropy actions of compact symmetric spaces.
To construct weakly reflective submanifolds in compact symmetric spaces,
we use symmetric triads which are generalizations of restricted root systems.


Yoshihiro Ohnita（OCAMI, Japan) 
Title:
Hamiltonian nondisplaceability of Gauss images
of isoparametric hypersurfaces (Joint work with
Hiroshi Iriyeh, Hui Ma and Reiko Miyaoka,)


Abstract:
In this talk we discuss the Hamiltonian nondisplaceability
of Gauss images of isoparametric hypersurfaces in the spheres
as Lagrangian submanifolds embedded in complex hyperquadrics.


