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
โฆ LIBER โฆ
Hypersurfaces in E4 with Harmonic Mean Curvature Vector Field
โ 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
No coin nor oath required. For personal study only.
โฆ Synopsis
The minimal hypersurfaces in E4 are the only hypersurfaces possessing the following property: Its mean curvature vector field is harmonic.
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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