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Hypersurfaces of E 4 with Harmonic Mean Curvature Vector
Author(s) -
Leuven Filip Defever Of
Publication year - 1998
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19981960104
Subject(s) - mathematics , mean curvature , hypersurface , submanifold , vector field , principal curvature , euclidean space , curvature , mathematical analysis , mean curvature flow , killing vector field , harmonic , pure mathematics , geometry , physics , quantum mechanics
A submanifold M n of a Euclidean space E m is said to have harmonic mean curvature vector field if Δ H , where H denotes the mean 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 hypersurface of E 4 with harmonic mean curvature vector field is minimal. The method gives insight in the role of the principal curvatures.
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