The third fundamental form metric for hypersurfaces in nonflat space forms |
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| Authors: | H. L. Liu U. Simon L. Verstraelen C. P. Wang |
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| Affiliation: | (1) Department of Mathematics, Northeast University, 110006 Shenyang, P.R. China;(2) TU Berlin, MA 8-3 Straße des 17. Juni 136, D-10623 Berlin;(3) Dep. Wiskunde KU Leuven, Celestijnenlaan 200 B, B-3001 Leuven;(4) Leopold;(5) Department of Mathematics, Beijing University, 100871 Beijing, P.R. China |
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| Abstract: | For hypersurfaces with regular Weingarten operator in nonflat space forms we study the relations between the intrinsic geometry of the third fundamental form metric and the extrinsic geometry of the hypersurface. We prove a theorema-egregium-type result for this metric and, in particular, give a local classification of hypersurfaces in case of an Einstein structure of this metric.Partially supported by the project 19701003 of NSFC.The geometry groops at TU Berlin and KU Leuven cooperate within the GA DGET program. |
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| Keywords: | 53 B 25 53 C 42 53 C 25 |
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