Journal of the Mathematical Society of Japan

Hypersurfaces of $E^4_8$ with proper mean curvature vector

Andreas ARVANITOYEORGOS, Filip DEFEVER, and George KAIMAKAMIS

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Abstract

Submanifolds satisfying Δ H = λ H are named by B. Y. Chen submanifolds with proper mean curvature vector. We prove that a hypersurface of the pseudo-Euclidean space E s 4 with Δ H = λ H and diagonalizable shape operator, has constant mean curvature.

Article information

Source
J. Math. Soc. Japan, Volume 59, Number 3 (2007), 797-809.

Dates
First available in Project Euclid: 5 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1191591858

Digital Object Identifier
doi:10.2969/jmsj/05930797

Mathematical Reviews number (MathSciNet)
MR2344828

Zentralblatt MATH identifier
1129.53018

Subjects
Primary: 53C40: Global submanifolds [See also 53B25]
Secondary: 53C50: Lorentz manifolds, manifolds with indefinite metrics 53A07: Higher-dimensional and -codimensional surfaces in Euclidean n-space

Keywords
biharmonic submanifold minimal hypersurface pseudo-Euclidean space

Citation

ARVANITOYEORGOS, Andreas; DEFEVER, Filip; KAIMAKAMIS, George. Hypersurfaces of $E^4_8$ with proper mean curvature vector. J. Math. Soc. Japan 59 (2007), no. 3, 797--809. doi:10.2969/jmsj/05930797. https://projecteuclid.org/euclid.jmsj/1191591858


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