Japanese / English
Osamu Ikawa (Kyoto Institute of Technology)
Yoshihiro Ohnita (Waseda University, OCAMI)
Shinji Ohno (Nihon University)
Naoyuki Koike (Tokyo University of Science)
Yuuki Sasaki (Utsunomiya University)
Hiroyuki Tasaki (Tokyo Metropolitan University, University of Tsukuba)
Makiko Sumi Tanaka (Tokyo University of Science)
Hiroshi Tamaru (Osaka Metropolitan University, OCAMI)
Masahiro Morimoto (Tokyo Metropolitan University)
13:00 - 13:40 Hiroyuki Tasaki: "Applications of Hermann Actions to disconnected compact Lie groups" 13:55 - 14:35 Shinji Ohno: "Polars and antipodal sets of generalized $s$-manifolds" 14:50 - 15:30 Hiroshi Tamaru: "Euler characteristics for quandles" 15:45 - 16:45 Osamu Ikawa: "The intersection of two real flag manifolds in a complex flag manifold, and symmetric triad" 17:00 - 18:00 Makiko Sumi Tanaka: "Compact symmetric spaces and antipodal sets"
9:10 - 9:50 Masahiro Morimoto: "The parallel transport map over affine symmetric space" 10:05 - 10:45 Yuuki Sasaki: "The isotropy group action of compact Hermitian symmetric spaces and Sasaki Einstein manifolds" 11:00 - 11:40 Naoyuki Koike: "Hyperpolar actions on the connection's space with the isometric gauge transformation group action and the holonomy map" [Abstract] 11:55 - 12:35 Yoshihiro Ohnita: "Totally Complex Submanifolds and $R$-spaces"
Yoshihiro Ohnita: "Totally Complex Submanifolds and $R$-spaces" This talk is based on a joint work with Kaname Hashimoto (Bunkyo U.& OCAMI) and Jong-Taek Cho (Chonnam National U.Korea). It is interesting to study special geometry of minimal submanifolds related to geometric structures of Riemannian manifolds. Totally complex subamanifolds of quaternionic K\"ahler manifolds also form one of such classes of minimal submanifolds. Recently we showed that any maximal dimensional totally complex submanifold of a quaternionic projective space with parallel second fundamental form can be obtained as the projection of a certain $R$-space associated with a quaternionic K\"ahler symmetric space under the Hopf fibration, based on differential geometric characterization of standardly embedded $R$-spaces due to Olmos-S\'anchez(1991). In this talk, using the structure of quaternionic K\"ahler symmetric spaces, we explain a classification of $R$-spaces which can be projected onto totally complex submanifolds of quaternionic projective spaces. In particular we obtain all maximal dimensional totally complex submanifold of a quaternionic projective space with parallel second fundamental form classified by Kazumi Tsukada(1985). Moreover, we discuss the corresponding homogeneous minimal Lagrangian submanifolds and the relation with the moment maps.
Naoyuki Koike: "Hyperpolar actions on the connection's space with the isometric gauge transformation group action and the holonomy map"
[Abstract]