## Journal of the Mathematical Society of Japan

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

#### Abstract

Submanifolds satisfying $\Delta \vec H = \lambda \vec H$ 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 $\Delta \vec H = \lambda \vec H$ 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

https://projecteuclid.org/euclid.jmsj/1191591858

Digital Object Identifier
doi:10.2969/jmsj/05930797

Mathematical Reviews number (MathSciNet)
MR2344828

Zentralblatt MATH identifier
1129.53018

#### 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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