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Title and Abstract of Talks：
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Katsuei Kenmotsu
（Tohoku University, Japan) |
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Title: A direct proof of Delaunay's Theorem and its generalization
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Abstract:
In 1841, Delaunay classified surfaces of revolution with constant mean curvature in a Euclidean
three space by an ingenious idea and later in 1981, Hsiang and Yu generalized it to higher
dimensions. In this talk, elementary proofs of these Theorems will be given.
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Megumi Harada
（McMaster University, Canada) |
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Title: Recent developments in the theory of Hamiltonian torus actions and integrable systems
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Abstract:
Hamiltonian torus actions play an essential role in equivariant symplectic geometry
and are closely related to other research areas,
such as toric varieties, representation theory, differential geometry, and combinatorics.
In this talk, I will give a broad overview of this subject for
non-experts, and then briefly describe some recent developments in this area,
with emphasis on the relationship with toric degenerations and Newton-Okounkov bodies.
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| Reiko Miyaoka
（Tohoku University, Japan) |
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Title: L^2 harmonic 1-forms on a complete stable minimal Lagrangian submanifolds
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Abstract:
We show that there exist no non-trivial L2 harmonic 1-forms on a complete non-compact stable minimal Lagrangian
submanifold in a Kahler manifold with positive Ricci curvature. In surface case, we give more details.
Also, we mention the H-stability problem given by B. Palmer.
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Chao Qian（University of Chinese Academy of Sciences, P.R. China)
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Title: Isoparametric functions on exotic spheres
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Abstract:
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Young Jin Suh （Kyoungpook National University, Korea) |
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Title: "Differential geometry of real hypersurfaces in complex quadrics"
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Abstract:
In this talk, first we classify real hypersurfaces with isometric Reeb flow in the complex quadric
$Q^m=SO_{m+2}/SO_mSO_2$, $m{\ge}3$.
We show that $m$ is even, say $m=2k$, and any such hypersurface is an open part of a tube around
a $k$-dimensional complex projective space $CP^k$ which is embedded canonically in $Q^{2k}$
as a totally geodesic complex submanifold.
It is known that a contact hypersurface in a K\"{a}hler manifold is a real hypersurface for which
the induced almost contact metric structure determines a contact structure.
From such a view point, next we carry out a systematic study of contact hypersurfaces in a K\"{a}hler manifolds.
We then apply these general results to obtain classifications of contact hypersurfaces with constant mean curvature
in the complex quadric $Q^n = SO_{n+2}/SO_nSO_2$
and its noncompact dual $Q^{n*} = SO^o_{n,2}/SO_nSO_2$ for $n \geq 3$.
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Imsoon Jeong and Young Jin Suh （Kyoungpook National University, Korea) |
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Title: "Some characterizations of Hopf hypersurfaces in complex two-plane Grassmannians related to the structure Jacobi operator"
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Abstract:
In this talk, we introduce a new notion of recurrent structure Jacobi operator, that is,
$(\nabla_{X}R_{\xi})Y=\omega(X)R_{\xi}Y$
for any tangent vector fields $X$ and $Y$ on a real hypersurface $M$ in complex two-plane Grassmannians $G_2({\mathbb C}^{m+2})$,
where $R_{\xi}$ denotes the structure Jacobi operator and $\omega$ a certain 1-form on $M$ in $G_2({\mathbb C}^{m+2})$.
Next, in $G_2({\mathbb C}^{m+2})$, we show that there does not exist any Hopf hypersurface $M$ with recurrent structure Jacobi
operator.
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Eunmi Pak and Young Jin Suh （Kyoungpook National University, Korea) |
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Title: "On parallelism for Jacobi operators in complex two-plane Grassmannians" |
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Abstract:
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Hyunjin Lee and Young Jin Suh （Kyoungpook National University, Korea) |
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Title: "Characterizations of real hypersurfaces in noncompact complex two-plane Grassmannians"
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Abstract:
A main objective in submanifold geometry is the classification of homogeneous hypersurfaces.
Homogeneous hypersurfaces arise as principal orbits of cohomogeneity one actions,
and so their classification is equivalent to the classification of cohomogeneity one actions up to orbit equivalence.
Actually, the classification of complex hyperbolic two-plane Grassmannains~$SU_{2,m}/S(U_{2}{\cdot}U_{m})$
which are cohomogeneity one actions in irreducible simply connected Riemannian symmetric spaces of noncompact type
was obtained by J. Berndt and Y.J. Suh (\textit{Hypersurfaces in noncompact complex Grassmannians of rank two},
International J. Math.~{\bf 23} (2012), 1250103, 35pp). From this classification, Suh classified real hypersurfaces
with isometric Reeb flow in $SU_{2,m}/S(U_{2}{\cdot}U_{m})$, $m \geq 2$. Each can be described as a tube over
a totally geodesic $\SU_{2,m-1}/S(U_{2}{\cdot}U_{m-1})$ in $SU_{2,m}/S(U_{2}{\cdot}U_{m})$ or a horosphere whose center
at infinity is singular (\textit{Hypersurfaces with isometric Reeb flow in complex hyperbolic two-plane Grassmannians},
Adv. in Appl. Math. {\bf 50} (2013), 645--659).
By using these results, in this talk we want to give another characterization for these model spaces
by the Reeb-invariant shape operator, that is, $\mathfrak L_{\xi}A=0$.
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Young Jin Suh and Changhwa Woo
（Kyoungpook National University, Korea) |
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Title:
Investigation of Hopf hypersurfaces with recurrent Ricci tensors in complex two plane Grassmannians
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Abstract:
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Gyu Jong Kim, Hyunjin Lee and Young Jin Suh
（Kyoungpook National University, Korea)
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Title:
Some classifications of Lie invariant Ricci tensor in complex two-plane Grassmannians
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Abstract:
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Doohyun Hwang, Hyunjin Lee and Changhwa Woo
（Kyoungpook National University, Korea)
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Title:
Semi-parallelism for real hypersurfaces in complex two-plane Grassmannians
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Abstract:
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Hiroshi Tamaru（Hiroshima University, Japan) |
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Title:
"An interaction between geometry of left-invariant metrics and group actions on symmetric spaces"
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Abstract:
For a given Lie group, the set of all left-invariant Riemannian metrics on it can naturally be regarded as
a noncompact Riemannian symmetric space. Then, there is a natural action of the automorphism group of the Lie group
on this symmetric space, which gives our interaction mentioned in the title.
In this talk, we describe this framework in more detail, and present several results on the interaction in both directions.
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Hironao Kato (OCAMI, Japan) |
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Title: Projectively and affinely flat manifolds from the viewpoint of
castling transformations, invariants and submanifolds.
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Abstract:
The main problem in my research project is to classify infinitesimal prehomogeneous vector spaces and left symmetric algebras.
Geometrically this problem is related to the existence problem of flat projective structures
and flat affine connections on manifolds.
In the talk firstly I will introduce a construction of projectively flat manifolds via Grassmannian structures
by using Cartan connections. Secondly I will focus our attention on Lie groups.
In particular I will discuss left invariant projectivey flat affine connections on products of special linear groups
and flat affine connections on parabolic subgroups of special linear groups form the viewpoint of relative invariants
and submanifolds.
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Shinobu Fujii (National Institute of Technology, Oshima, Japan) |
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Title: Moment maps and isoparametric hypersurfaces in spheres---Grassmannian cases
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Abstract:
We are studying a relationship between isoparametric hypersurfaces in spheres with four distinct
principal curvatures and moment maps of certain Hamiltonian actions. In this talk, we consider the
isoparametric hypersurfaces obtained from the isotropy representations of Grassmannian manifolds of
rank two.
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Akira Kubo (Hiroshima University, Japan) |
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Title: "Geometry of polar actions on complex hyperbolic spaces"
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Abstract:
We are interested in geometry of homogeneous submanifolds in symmetric spaces of noncompact type.
In this talk, we will focus on orbits of polar actions without singular orbits
on complex hyperbolic spaces, and introduce our results on their minimality.
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