Lecture Notes on Symmetric Spaces
نویسنده
چکیده
1. Definition and Examples (p.2) 2. Transvections and Holonomy (p.7) 3. Killing Fields (p.9) 4. Cartan Involution and Cartan Decomposition (p.11) 5. Locally Symmetric Spaces (p.15) 6. Compact, Noncompact and Euclidean Type; Duality (p.16) 7. The Isometry Group (p.17) 8. Lie Subtriples and Totally Geodesic Subspaces (p.19) 9. Isotropy Representation and Rank (p.19) 10. The Weyl Group (p. 22) References (p.24)
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These are lecture notes on the rigidity of submanifolds of projective space " resembling " compact Hermitian symmetric spaces in their homogeneous embeddings. are surveyed, along with their classical predecessors. The notes include an introduction to moving frames in projective geometry, an exposition of the Hwang-Yamaguchi ridgidity theorem and a new variant of the Hwang-Yamaguchi theorem.
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These are lecture notes on the rigidity of submanifolds of projective space “resembling” compact Hermitian symmetric spaces in their homogeneous embeddings. The results of [16, 20, 29, 18, 19, 10, 31] are surveyed, along with their classical predecessors. The notes include an introduction to moving frames in projective geometry, an exposition of the Hwang-Yamaguchi ridgidity theorem and a new v...
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Permission to make copies of these lecture notes for educational or scientific use, including multiple copies for classroom or seminar teaching, is granted (without fee), provided that any fees charged for the copies are only sufficient to recover the reasonable copying costs, and that all copies include this title page and its copyright notice. Specific permission of the author is required to ...
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1. S. GiNDiKrN, 'Analysis on homogeneous domains', Russian Math. Surveys 19 (1964) 1-89. 2. M. KOECHER, 'An elementary approach to bounded symmetric domains', Lecture Notes, Rice University, 1969. 3. O. Loos, 'Bounded symmetric domains and Jordan pairs', Lecture Notes, University of California, Irvine, 1977. 4. A. UNTERBERGER and H. UPMEIER, Pseudodifferential analysis on symmetric cones (CRC-P...
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