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: unparalleled uncomplicated Lie teams and comparable themes in contemporary Differential Geometry.- U. Simon: Dirichlet difficulties and the Laplacian in Affine Hypersurface Theory.- Wang Shicheng: crucial Invariant Circles of floor Automorphism of Finite Order.
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Additional resources for Differential Geometry and Topology: Proceedings of the Special Year at Nankai Institute of Mathematics, Tianjin, PR China, 1986–87
Soc. 15 (1983), 493-498. Thomas E. C e c i l Department of Mathematics C o l l e g e o f t h e Holy C r o s s Worcester, MA 01610 Shiing-Shen Chern Department of Mathematics University of California B e r k e l e y , CA 94720 and Mathematical Sciences Research 1000 C e n t e n n i a l D r i v e B e r k e l e y , CA 94720 Institute THE MEAN CURVATURES HYPERSURFACES OF CONSTANT ON THE IN A TUBULAR SPACE CURVATURE Chen Weihuan* Recently the structure of focal sets of hypersurfaces in the space of constant curvature has been intensively studied (cf.
2), which is closely related to the geometry of the tubular hypersurfaces of submanifolds. In their discussion the spaces of constant curvature are usually considered as hypersurfaces in a Euclidean space or a pseudo-Euclidean space. In this paper, we shall first give the metric and the second fundamental form of the tubular hypersurface around a submanifo]d ~n the space of constant curvature using the technique of Jacobi fields, and then we shall give the formulas to the integral of mean curvatures over the tubular hypersurfaces, which are the generalizations of the well-known area formulas of the tubular hypersurfaces given by H.
Of e. at field satisfying Yi(0) and the one corresponding DY. 17) In this case we have Yi(~) = (exp~),~(Xi), X =u~ X B, of course, is the vertical ing N-Jacobi Y (~) = ( e x p v ) ~ ( X ) . 18) to a s, so the correspond- field is Ya = u a~ YB " In particular Ym(S) = (exp~),~(Xm) = Em(S ). lae , ~(%~)2 = I. 1) From the following proposition we know that Ym(g)=Em(S) is the unit normal vector field to N . ,~ Y~ along XV defined as in §i satisfy Y1 ( ~)A'''AYn(~)iYn+ I(~)A'-'AYm_ I(E:) = O. 2) Let J denote the Jacobian of map exp~ at ~.
Differential Geometry and Topology: Proceedings of the Special Year at Nankai Institute of Mathematics, Tianjin, PR China, 1986–87 by Thomas E. Cecil, Shiing-Shen Chern (auth.), Boju Jiang, Chia-Kuei Peng, Zixin Hou (eds.)