Title and Abstract of Talks：
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Kazumi Tsukada
（Ochanomizu University, Japan) 
Title: Totally complex submanifolds of a complex Grassmann manifold of 2planes


Abstract:
A complex Grassmann manifold ${\rm G}_2 (\mathbb{C}^{m+2})$ of all $2$dimensional complex subspaces in
$\mathbb{C}^{m+2}$ has two nice geometric structures  the K\"ahler structure and
the quaternionic K\"ahler structure.
We study totally complex submanifolds of ${\rm G}_2 (\mathbb{C}^{m+2})$ with respect to
the quaternionic K\"ahler structure.
We show that the projective cotangent bundle ${\rm P}(T^* \mathbb{C}P^{m+1})$ of
a complex projective space $\mathbb{C}P^{m+1}$ is a twistor space of the quaternionic K\"ahler manifold
${\rm G}_2 (\mathbb{C}^{m+2})$.
Applying the twistor theory, we construct maximal totally complex submanifolds of
${\rm G}_2 (\mathbb{C}^{m+2})$ from complex submanifolds of $\mathbb{C}P^{m+1}$.
Then we obtain many interesting examples.
In particular we classify maximal homogeneous totally complex submanifolds.
We show the relationship between the geometry of complex submanifolds of $\mathbb{C}P^{m+1}$ and
that of totally complex submanifolds of ${\rm G}_2 (\mathbb{C}^{m+2})$.
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Yong Seung Cho（Ewha Women's University, Korea)

Title: GromovWitten Invariants on Symplectic Fibrations


Abstract:
We construct a symplectic fibration over almost contact metric manifolds with symplectic fibre.
The total space of the fibration has an almost contact metricstructure with a group of symplectomorphisms
of the fibre.
If the fibre is simply connected, then the flux homomorphism is trivialand the total space has
a coupled connection 2form. We construct the coupled connection 2form and investigate the form.
When the connection of a fibration is flat,
we study the properties of total space and base space.
As a trivial case we consider the products of almost contact metric manifolds and symplectic manifolds.
We study GromovWitten type invariants and quantum type cohomologies o f the products.
As an example we consider the product of the 3sphere and a CalabiYau 3fold.


Wayne Rossman and Masashi Yasumoto
（Kobe University, Japan) 
Title: Singularities of discretized linear Weingarten surfaces


Abstract:
In this talk we will explain singularities of discretized surfaces
with special curvature conditions. In particular, singularities of
discrete and semidiscrete maximal surfaces in LorentzMinkowski
3space and singularities of discrete linear Weingarten surfaces
of Bryant and Bianchi types will be discussed.


Mayuko Kon
（Shinshu University, Japan) 
Title: Shape operator of real hypersurfaces in a 2dimensional complex space form

Abstract:
We show that if a shape operator of a real hypersurface in a 2dimensional complex space form satisies
a transversal Killing equation, then it is locally conguent to a geodesic hypersphere.
Moreover, we introduce some nonHopf hypersurfaces which satisfies g(AX,Y)=ag(X,Y)
for some function a and any vector field X and Y orthogonal to the structure vector field.
This result is an example of nonHopf real hypersurfaces given by IveyRyan, 2011.




J\"urgen Berndt (King's College London, UK) and
Young Jin Suh*（Kyungpook National University, Korea)

Title: Differential geometry of real hypersurfaces in Hermitian symmetric spaces with rank 2


Abstract:
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Juan De Dios Perez (University de Granada, Spain) and
Changhwa Woo* (Kyungpook National University, Korea) 
Title: Hopf hypersurfaces in complex twoplane Grassmannians with GTW connections


Abstract:
In this talk, we will give some nonexistence properties for Hopf real hypersurfaces in complex twoplane Grassmannians with certain geometric conditions.
First, real hypersurfaces in complex twoplane Grassmannians with generalized TanakaWebster recurrent shape operator $A$ will be talked
in detail. Next, harmonic curvature with generalized TanakaWebster connection for Hopf hypersurfaces in complex twoplane Grassmannians and its related topics will be given.
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Hyunjin Lee
（SRCGAIA, POSTECH, Korea)

Title:
A real hypersurface in complex twoplane Grassmannians with recurrent (1,1)type tensor


Abstract:
Kobayashi and Nomizu [Foundations of Differential Geometry, Vol. I] have introduced a notion of recurrent
for (r,s) type tensor on Riemannian manifolds. By the definition, we see that the conception of recurrent
naturally becomes a kind of generalized parallelism. Specifically, we consider this notion for
(1,1) type tensor defined on a real hypersurface in complex twoplane Grassmannians.
Among several (1,1) type tensors, let us consider a structure Jacobi operator given on the Riemannian
curvature tensor in this talk. Actually, Jeong, Perez and Suh [Acta Math. Hungar. (2009)] verified that
there does not exist any connected Hopf hypersurface in complex twoplane Grassmannians with
parallel structure Jacobi operator. We consider more general notions, which are said to be Reeb or
$\mathcal Q^{\bot}$recurrent structure Jacobi operator. By using these two weaker conditions,
we give some characterizations of Hopf hypersurfaces in complex twoplane Grassmannians.
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Eunmi Pak（Kyungpook National University, Korea) 
Title: Study on structure Jacobi operator in complex twoplane Grassmannians 

Abstract:
We study classifying problems of real hypersurfaces in a complex twoplane Grassmannian
$G_2({\mathbb C}^{m+2})$. In relation to structure Jacobi operator, we consider some recurrent condition.
In this case, we prove a complete classification for a real hypersurface
in $G_2({\mathbb C}^{m+2})$ satisfying such a condition.
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Gyujong Kim* and Young Jin Suh
（Kyungpook National University, Korea)

Title: Real hypersurfaces in complex twoplane Grassmannians with GTW Lie derivative structure Jacobi operator


Abstract:
In this talk, several kinds of structure Jacobi operator tensors are defined on a Real hypersurface M
in complex twoplane Grassmannians $G_{2}(C^{m+2})$. Using Berndt and Suh's theory, we give some complete classifications of M
in $G_{2}(C^{m+2})$ with these conditions about GTW Lie derivative structure Jacobi operator.
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Imsoon Jeong*（Kyungpook National University, Korea) 
Title: Parallelism of normal Jacobi operator for real hypersurfaces in complex twoplane Grassmannians


Abstract:
In this talk, we introduce a notion of normal Jacobi operator $\RN$ for
hypersurfaces $M$ in a complex twoplane Grassmannians $G_2({\Bbb C}^{m+2})$ in such a way that
$${\RN}X={\bar R}(X,N)N{\in}\text{End}\ (T_xM), \quad x{\in}M$$
for any tangent vector field $X$ on $M$, where $\bar R$ and $N$ respectively denote the Riemannian
curvature tensor and a
unit normal vector field of $M$ in $G_2({\Bbb C}^{m+2})$. The ambient space $G_2({\Bbb C}^{m+2})$
has a remarkable geometric structure. It was known that $G_2({\Bbb C}^{m+2})$
is the unique compact irreducible Riemannian symmetric space equipped with both a
K\"{a}hler structure $J$ and a quaternionic K\"{a}hler structure
${\frak J}$. And the structure vecror field $\xi$, $\xi = J N$, of a real hypersurface $M$ in
$G_2({\Bbb C}^{m+2})$ is said to be a {\it Reeb vector field}.
The almost contact structure vector fields $\{\xi_1
,\xi_2 ,\xi_3 \}$ are defined by $\xi_i =J_i N$, $i=1,2,3$, where
$\{J_1, J_2, J_3\}$ denote a canonical local basis of quaternionic
K\"ahler structure ${\frak J}$ on $G_2({\Bbb C}^{m+2})$. If the distributions $\frak D$ and ${\frak
D}^{\bot}=\text{Span}\{{\xi}_1,{\xi}_2,{\xi}_3\}$ are invariant by
the shape operator $A$ of $M$, that is, $g(A{\frak D}, {\frak
D}^{\bot})=0 $, where $T_xM = {\frak D}{\oplus}{\frak D}^{\bot}$,
$x{\in}M$, then we call $M$ is ${\frak D}^{\bot}$invariant.
The normal Jacobi operator $\RN$ is said to be {\it Reeb parallel} on $M$ if the covariant derivative of the normal
Jacobi operator ${\bar R}_N$ along the direction of the Reeb vector
$\xi$ identically vanishes, that is, ${\nabla}_{\xi}{\RN} = 0$ .
\vskip 6pt
Related to such a Reeb parallel normal Jacobi operator ${\RN}$, we give a complete
classification of ${\frak D}^{\bot}$invariant real hypersurfaces in
complex twoplane Grassmannians $G_2({\Bbb C}^{m+2})$ with Reeb parallel normal Jacobi operator.
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Wenjiao Yan（Beijing Normal University, P.R. China & Tohoku University, Japan) 
Title:
Isoparametric foliation in spheres and Yau's conjecture on the first eigenvalue


Abstract:
I will give a brief introduction of the isoparametric foliation in spheres and
talk about our recent works on this subject related with Yau conjecture,
which states that the first eigenvalue of every closed minimal embedded
hypersurface in the unit sphere is its dimension.


Tohru Kajigaya（Tohoku University & OCAMI, Japan) 
Title:
Hamiltonian minimality of normal bundles over the isoparametric submanifolds


Abstract:
A Hamiltonian minimal (shortly, Hminimal) Lagrangian submanifold in a Kahler manifold is a critical point of
the volume functional under all compactly supported Hamiltonian deformations.
This gives a nice extension of the notion of minimal submanifolds.
In this talk, we focus on constructions of Hminimal Lagrangian submanifolds
in the complex Euclidean space C^n.
We show that any normal bundle of a principal orbit of the adjoint representation of
a compact simple Lie group G in the Lie algebra g of G is an Hminimal Lagrangian submanifold
in the tangent bundle Tg which is naturally regarded as C^n.
Moreover, we specify these orbits with this property
in the class of full irreducible isoparametric submanifolds in the Euclidean space.


Kaname Hashimoto (OCAMI, Japan) 
Title: Special Lagrangian submanifolds invariant under the isotropy action of
symmetric spaces of rank 2


Abstract:
In this talk we will explain the construction of cohomogenity one
special Lagrangian submanifolds in the cotangent bundle of the sphere in
the tangent space of Riemannian symmetric spaces of rank 2.


Takahiro Hashinaga
（Hiroshima University, Japan) 
Title: On local isometric embeddings of lowdimensional Lie groups


Abstract:
It is classically well known that any Riemannian manifold can be locally
isometrically embedded into the Euclidean spaces of sufficiently large dimension.
We are interested in determining the least dimension of Euclidean spaces
into which the given Riemannian manifolds can be locally isometrically embedded.
In this talk, we will classify leftinvariant Riemannian metrics on
threedimensional Lie groups which can be locally isometrically embedded
into the fourdimensional Euclidean space.


Akira Kubo
（Hiroshima University, Japan) 
Title: Totally geodesic submanifolds in some symmetric spaces


Abstract:
Classification of totally geodesic surfaces in Riemannian symmetric
spaces is one of the most fundamental problems in submanifold geometry.
As a first step of our studies, we focus on the case of the symmetric
space of type AI. In this talk, we prove that totally geodesic surfaces
in such spaces correspond to certain nilpotent matrices, and as
applications we give the explicit classifications in the cases of low rank.


Volker Branding (University of Vienna, Austria) 
Title: The evolution equation for magnetic geodesics


Abstract:
Magnetic geodesics describe the trajectory of a particle in a
Riemannian manifold subjected to an external magnetic field.
We use the heat flow method to deform a given curve and discuss in
which cases we obtain a nontrivial magnetic geodesic.
This is joint work with Florian Hanisch.


Wolfgang Carl
（TUGraz University, Austria) 
Title: Calculus of variations on semidiscrete surfaces


Abstract:
A semidiscrete surface is represented by a mapping into
threedimensional Euclidean space possessing one discrete and one
continuous variable. It can be seen as a semidiscretization of a
smooth surface, or as a partial limit case of a purely discrete
surface, i.e., a mesh. In this talk we use variational principles
to establish the following objects on semidiscrete surfaces:
(i) a Laplace operator by variation of the Dirichlet energy
functional, (ii) a mean curvature vector field by variation of the
surface area, and (iii) a normal vector field by variation of the
enclosed volume. Subsequently we analyze the properties of these
objects, their connections with each other, and their convergence
behavior. As examples of possible applications we discuss
semidiscrete harmonic functions and semidiscrete surfaces of
revolution with constant mean curvature.


Yuta Ogata（Kobe University, Japan) 
Title:Criteria for singularities of spacelike constant mean curvature surfaces
in Lorentzian spaceforms


Abstract:
In this talk, we will explain singularities of spacelike constant
mean curvature (CMC) surfaces in Lorentzian spaceforms. Unlike the case in
Riemannian spaceforms, spacelike CMC surfaces in these spaceforms
generally have singularities. After introducing the Lax representations
for spacelike CMC surfaces, we will give criteria for their singularities.
At the end of our talk, we will show some examples of spacelike CMC
surfaces with singularities.


Keisuke Teramoto（Kobe University, Japan) 
Title:Parallel surfaces of cuspidal edges


Abstract:
We investigate parallel surfaces of cuspidal edges.
We give a criterion for the parallel surfaces of cuspidal edges to
have swallowtail singularities. Moreover, we also clarify
relations between singularities of parallel surfaces and
differential geometric properties of initial cuspidal edges.


Saki Okuhara (OCAMI, Japan) 
Title: Geometry associated to the tt*Toda equation


Abstract:
Guest and Lin proved the existence of a smooth and global solution to the tt*Toda equation.
In this talk, I explain their result and possible applications
to the construction of minimal submanifolds asuch as special Lagrangian cones.


Shinji Ohno and Takashi Sakai (Tokyo Metropolitan University, Japan) 
Title: Areaminimizing cones over minimal embeddings of Rspaces


Abstract:
Solutions of Plateau's problem may have singularities as integral currents.
At an isolated conical singularity, the tangent cone is areaminimizing.
Hence, in order to understand such singularities, we should study areaminimizing properties of minimal cones.
In this talk, by constructing areanonincreasing retractions, we discuss areaminimizing properties of
some cones over minimal embeddings of Rspaces.


Yoshihiro Ohnita (Osaka City University & OCAMI, Japan) 
Title: Lagrangian intersection theory of the Gauss images of isoparametric hypersurfaces
(ioint work with Hiroshi Iriyeh, Hui Ma and Reiko Miyaoka)


Abstract:
The Gauss images of isoparametric hypersurfaces in the standard unit sphere provide
a nice class of compact minimal Lagrangian submanifolds embedded in the complex hypquadrics.
In this talk I report new results on the Hamiltonian nondisplaceability of
the Gauss images of isoparametric hypersurfaces in the joint work with
Hiroshi Iriyeh, Hui Ma and Reiko Miyaoka.

