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Hypersurfaces of E4 with Harmonic Mean Curvature Vector

✍ Scribed by Filip Defever Of Leuven

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 362 KB
Volume: 196
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19981960104

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✦ Synopsis

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 give a proof of the theorem that every hypereurface of E' with harmonic mean curvature vector field is minimal. The method gives insight in the role of the principal curvatures.

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