"A new approach to conformal maps between Riemannian manifolds from a viewpoint of a variational problem"
"On totally geodesic surfaces in symmetric spaces and applications"
"On geometrical structures on $G_2/SO(4)$"
"Edge-cone Einstein metrics and the Yamabe invariant"
"Ruled real hypersurfaces having the same sectional curvature as that of an ambient nonflat complex space form"
"Grassmann geometry of 3-dimensional homogeneous spaces"
"Transversally complex submanifolds of a quaternion projective space"
"Grassmann geometry and symmetric space"
10:00-10:50 川上 裕 (金沢大学)
"On the Gauss image of complete minimal surfaces in Euclidean 4-space"
11:05-11:55 伊師英之 (名古屋大学)
"On Hessian metrics with group invariance"
13:30-14:20 Jürgen Berndt (King's College London / 広島大学)
"The index of symmetric spaces"
A well-known result, first proved by Iwahori, states that an irreducible Riemannian symmetric space admitting a totally geodesic hypersurface must be a space of constant curvature.
Onishchik introduced the index of a Riemannian symmetric space M as the minimal codimension of a totally geodesic submanifold of M.
He then gave an alternative proof for Iwahori's result and also classified the irreducible Riemannian symmetric spaces with index 2.
He also determined the index of Riemannian symmetric spaces of rank 2.
In the talk I will present some new ideas and results on the index of Riemannian symmetric spaces.
The new methods allow us to calculate the index for many, but not all, irreducible Riemannian symmetric spaces M.
As a consequence we also obtain the classification of all non-semisimple maximal totally geodesic submanifolds of M.
We also show that the index is bounded from below by the rank of M, and classify all M for which the index coincides with the rank.
This is joint work with Carlos Olmos (Cordoba).
14:35-15:25 間下克哉 (法政大学)
"Invariant forms on $SU(4)$"