Cylindricity of complete Euclidean submanifolds with relative nullity

作者: Felippe Soares Guimarães , Guilherme Machado de Freitas

DOI: 10.1007/S10455-015-9490-0

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摘要: We show that a complete Euclidean submanifold with minimal index of relative nullity \(\nu _0>0\) and Ricci curvature certain controlled decay must be _0\)-cylinder. This is an extension the classical Hartman cylindricity theorem.

参考文章(8)
John Douglas Moore, Isometric immersions of riemannian products Journal of Differential Geometry. ,vol. 5, pp. 159- 168 ,(1971) , 10.4310/JDG/1214429785
William Wylie, A warped product version of the Cheeger-Gromoll splitting theorem arXiv: Differential Geometry. ,(2015)
E. García-Río, D. N. Kupeli, B. Ünal, M. Fernández-López, A curvature condition for a twisted product to be a warped product Manuscripta Mathematica. ,vol. 106, pp. 213- 217 ,(2001) , 10.1007/S002290100204
Robert Maltz, Cylindricity of isometric immersions into Euclidean space Proceedings of the American Mathematical Society. ,vol. 53, pp. 428- 432 ,(1975) , 10.1090/S0002-9939-1975-0643658-X
Dirk Ferus, On the completeness of nullity foliations. The Michigan Mathematical Journal. ,vol. 18, pp. 61- 64 ,(1971) , 10.1307/MMJ/1029000589
Francisco Vittone, On the nullity distribution of a submanifold of a space form Mathematische Zeitschrift. ,vol. 272, pp. 1- 16 ,(2012) , 10.1007/S00209-011-0918-3
Ioannis Argyros, Gary Huckabay, Mohammad Tabatabai, OF PURE AND APPLIED MATHEMATICS ,(2003)
Carlos Olmos, Francisco Vittone, On completeness of integral manifolds of nullity distributions Revista De La Union Matematica Argentina. ,vol. 53, pp. 89- 90 ,(2011)