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Universität Augsburg
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Universität Augsburg
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Professor Dr. Yoshihiro Ohnita
Global Center for Science and Engineering, Waseda University & OCAMI, Osaka Metropolitan University, Japan
spricht am
Mittwoch, 25. März 2026
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11 Uhr s.t.
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
| This talk is based on my joint work with Jong Taek Cho (Chonnam Natl.U.,Korea) and Kaname Hashimoto (OCAMI/Bunkyo Univ.,Japan). It is fundamental in differential geometry to study special geometry of minimal submanifolds related to the underlying geometric structures of a Riemannian manifold. Totally complex submanifolds of quaternionic Kähle manifolds form a distinguished class of minimal submanifolds. They are minimal submanifolds covered by horizontal and complex submanifolds in the associated twistor spaces. In this work we construct a new, non Levi- Civita, canonical connection on the inverse image of any maximal dimensional totally complex submanifold of the quaternionic projective space under the Hopf fibration. As its application, based on the theorem of Olmos and Sánchez (J. reine angew. Math., 1991), we provide a geometric proof that any maximal dimensional totally complex submanifold of the quaternionic projective space with parallel second fundamental form arises as the projection of a certain singular $R$-space associated with a quaternionic Kähler symmetric space under the Hopf fibration. By the Lie algebraic structure of quaternionic Kähler symmetric pairs, we determine such $R$-spaces explicitly and, in particular, recover all maximal dimensional totally complex submanifolds of quaternionic projective spaces with parallel second fundamental form, previously classified by Tsukada (Osaka J. Math., 1985) by a different method. Moreover, we discuss additional geometric properties of those totally complex submanifolds, such as their fundamental groups, weak reflectivity, associated moment maps and Lagrangian submanifolds. |
| Hierzu ergeht herzliche Einladung. |
| Peter Quast |
Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).