The Gauss Equations and Rigidity of Isometric Embeddings
نویسنده
چکیده
0. Introduction (a) Statements of main results 804 (b) Discussion of sections 1, 2 805 (c) Discussion of section 3 806 (d) Discussion of section 4 808 (e) Discussion of section 5 809 1. Basic structure equations (a) Structure equations of Riemannian manifolds 810 (b) Structure equations of submanifolds of Euclidean space 814 2. The isometric embedding system (a) Setting up the system 823 (b) Proof of the Burstin-Cartan-Janet-Schaefly (BCJS) theorem .830 3. Localization of the Gauss equations (a) Proof of (i) and (ii) in the Main Theorem 835 (b) Proof of (iii) in the Main Theorem 842 4. Nongeneric behavior of the Gauss equations (a) Exteriorly orthogonal forms 855 (b) Isometric embedding of space forms and similar metrics 859 5. The Gauss equations and the GL(n)-representation theory of tensors (a) Introduction 870 (b) GL(n) and the symmetric group actions 871 (c) Representations of algebras 872 (d) The regular representation of FSq 874 (e) GL(V*)-irreducible subspaces of (qv* 878 (f) Decomposition of the tensor product: the Littlewood-Richardson rule 879 (g) The spaces K =/()i " 1) 881 (h) The Gauss equations: an equivariant approach 884 References 892
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