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Universität Augsburg
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Universität Augsburg
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Professor Dr. Makiko Tanaka
Tokyo University of Science
spricht am
Donnerstag, 28. März 2019
um
14:00 Uhr
im
Raum 1009 (L1)
über das Thema:
| Abstract: |
| A compact Lie group G with biinvariant metric is a Riemannian symmetric space. Each connected component of the geodesic symmetry sx at x∈G is called a polar of G with respect to x. For example, a polar of the orthogonal group O(n) with respect to the identity matrix can be regarded as the real Grassmann manifold of the k-dimensional subspaces in ℝn for some k. A polar is a totally geodesic submanifold, hence a Riemannian symmetric space with respect to the induced metric and its geodesic symmetries are the restriction of geodesic symmetries on G. On the other hand, a subset A of a compact Riemannian symmetric space is called an antipodal set if sx(y)=y holds for any x,y∈A. Our aim is to classify maximal antipodal sets of compact Riemannian symmetric spaces and to determine the ones whose cardinalities attains the maximum. When a compact Riemannian symmetric space M can be realized as a polar of a compact Lie group G, by using some relation between the conjugacy classes of maximal antipodal subgroups of G and the congruence classes of maximal antipodal sets of M, we can obtain the classification. In this talk I will explain it in some concrete cases. This talk is based on a joint work with Hiroyuki Tasaki. |
| Hierzu ergeht herzliche Einladung. |
| Peter Quast |
Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn in L-1009