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Hypersurfaces in E4 with Harmonic Mean Curvature Vector Field

โœ Scribed by Th. Hasanis; Th. Vlachos


Publisher
John Wiley and Sons
Year
1995
Tongue
English
Weight
859 KB
Volume
172
Category
Article
ISSN
0025-584X

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โœฆ Synopsis


The minimal hypersurfaces in E4 are the only hypersurfaces possessing the following property: Its mean curvature vector field is harmonic.


๐Ÿ“œ SIMILAR VOLUMES


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A submanifold M" of a Euclidean space Em is said to have harmonic mean curvature vector field if A# = a, where denotes the mern curvature vector. B. -Y. CHEN conjectured that the only submanifolds of Euclidean spaces with harmonic mean curvature vector field, are the minimal ones. In this paper, we

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In this article, we prove the following theorem: A complete hypersurface of the hyperbolic space form, which has constant mean curvature and non-negative Ricci curvature Q, has non-negative sectional curvature. Moreover, if it is compact, it is a geodesic distance sphere; if its soul is not reduced