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Isometric Immersions into Warped Product Spaces

Isometric Immersions into Warped Product Spaces
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摘要 This paper concerns the submanifold geometry in the ambient space of warped productmanifolds F^n×σ R, this is a large family of manifolds including the usual space forms R^m, S^m and H^m. We give the fundamental theorem for isometric immersions of hypersurfaces into warped product space R^n×σ R, which extends this kind of results from the space forms and several spaces recently considered by Daniel to the cases of infinitely many ambient spaces. This paper concerns the submanifold geometry in the ambient space of warped productmanifolds F^n×σ R, this is a large family of manifolds including the usual space forms R^m, S^m and H^m. We give the fundamental theorem for isometric immersions of hypersurfaces into warped product space R^n×σ R, which extends this kind of results from the space forms and several spaces recently considered by Daniel to the cases of infinitely many ambient spaces.
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2010年第12期2269-2282,共14页 数学学报(英文版)
基金 Supported by National Natural Science Foundation of China (Grant No. 10871149) Doctoral Fund of Education of China (Grant No. 200804860046)
关键词 Isometric immersion HYPERSURFACE warped product the fundamental theorem Isometric immersion, hypersurface, warped product, the fundamental theorem
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参考文献14

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