the supporters' association of Faculty of Science,
Korikai (the alumni association of Faculty of Science).
Programme
Saturday, 5 March
15:00-15:05
Opening Address
15:05-15:55
Nobumitsu Nakauchi (Yamaguchi University)
"A new approach to conformal maps between Riemannian manifolds from a viewpoint of a variational problem"
16:10-17:00
Hiroshi Tamaru (Hiroshima University)
"On totally geodesic surfaces in symmetric spaces and applications"
17:15-18:05
Hideya Hashimoto (Meijo University)
"On geometrical structures on $G_2/SO(4)$"
Sunday, 6 March
10:00-10:50
Kazuo Akutagawa (Tokyo Institute of Technology)
"Edge-cone Einstein metrics and the Yamabe invariant"
11:05-11:55
Sadahiro Maeda (Saga University)
"Ruled real hypersurfaces having the same sectional curvature as that of an ambient nonflat complex space form"
14:00-14:50
Jun-ichi Inoguchi (University of Tsukuba)
"Grassmann geometry of 3-dimensional homogeneous spaces"
15:05-15:55
Kazumi Tsukada (Ochanomizu University)
"Transversally complex submanifolds of a quaternion projective space"
16:10-17:00
Hiroo Naitoh (Yamaguchi University)
"Grassmann geometry and symmetric space"
Monday, 7 March
10:00-10:50 Yu Kawakami (Kanazawa University)
"On the Gauss image of complete minimal surfaces in Euclidean 4-space"
11:05-11:55 Hideyuki Ishi (Nagoya University)
"On Hessian metrics with group invariance"
13:30-14:20 Jürgen Berndt (King's College London / Hiroshima University)
"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 Katsuya Mashimo (Hosei University)
"Invariant forms on $SU(4)$"