By Thomas E. Cecil, Shiing-Shen Chern (auth.), Boju Jiang, Chia-Kuei Peng, Zixin Hou (eds.)
From the contents: T.E. Cecil, S.S. Chern: Dupin Submanifolds in Lie Sphere Geometry.- R.L. Cohen, U. Tillmann: Lectures on Immersion Theory.- Li An-Min: Affine Maximal floor and Harmonic Functions.- S. Murakami: unheard of easy Lie teams and similar themes in fresh Differential Geometry.- U. Simon: Dirichlet difficulties and the Laplacian in Affine Hypersurface Theory.- Wang Shicheng: crucial Invariant Circles of floor Automorphism of Finite Order.
Read or Download Differential Geometry and Topology: Proceedings of the Special Year at Nankai Institute of Mathematics, Tianjin, PR China, 1986–87 PDF
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Extra resources for Differential Geometry and Topology: Proceedings of the Special Year at Nankai Institute of Mathematics, Tianjin, PR China, 1986–87
F . Mhnzner, Isouarametrische Hvnerfl~chen in Sohhren. I and I f , Math. Ann. 251 (1980), 57-71 and 256 (1981), 215-232. [N] K. cg~, Lin. and Multilin. Alg. 2 (1973), 159-162. [P1] [P2] [P3] IS] U. Pinkail, DuDin'sche HvDerfl~chen, D i s s e r t a t i o n , Univ. Freiburg, 1981. , Duuin'sche Hvuerfl~chen in E4, Manuscr. Math 51 (1985), 89-119. . . , Duuin hv~ersurfaces, Math. Ann. 270 (1985), 427-440. D. Slngley, Smoothness theorems for the ~rinciual curvatures and Drlncinal vectors of a hvnersurface, Rocky Mountain d.
Lemma 4 At each point x ~ N, the average of H (v) when v passes over the whole q unit sphere Sp-I in the normal subspace Vx(N) is Kc 2D i I ~ J H (v)dO Op_ 1 s P _ l q = , if q=2p, ( 2H) n p(p+2) •.. 5) p - I~ 0, if q is odd. where Op_ I is the total area of Sp-I and Kc 1 2H "6~I"''~2~ 22Pp! O2p "''Kq %li2JlJ2 - . 6) Kc ijkl = Rijkl c(6ik6jl-6il6jk )" Rijkl is the curvature tensor of N. 5) should be understood to be I. -. - A (W~+~x%~) q! q! -. qp! I.. (%m~Pf~(q 1 •. 8) 50 ~(ql'" "'qp) = iq 61 ....
46) terms that allow of p simpler This and of p is is Pinkall's never our first never vanishes all p. of derivatives proof than Pinkall p on gave on B. B. The Lemma [ P 2 , function one to e x p r e s s its zero p, Since following 108], p # the second Pa' This where O, the covariant enables us for the lemma. Then Pl " P2 = P3 ~ 0 at B. 46) identically. 34 We now complete everywhere. 25), that the expression P3 must vanish s12 - s 2 1 . we h a v e s12 - s21 = - 2 s P 3 - p s 3 • By ( 5 . 4 6 ) and ( 5 .