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Biharmonic Submanifolds with Parallel Mean Curvature Vector in Pseudo-Euclidean Spaces

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Abstract

In this paper, we investigate biharmonic submanifolds in pseudo-Euclidean spaces with arbitrary index and dimension. We give a complete classification of biharmonic spacelike submanifolds with parallel mean curvature vector in pseudo-Euclidean spaces. We also determine all biharmonic Lorentzian surfaces with parallel mean curvature vector field in pseudo-Euclidean spaces.

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Authors and Affiliations

  1. School of Mathematics and Quantitative Economics, Dongbei University of Finance and Economics, Dalian, 116025, Peoples Republic of China

    Yu Fu

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  1. Yu Fu
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Correspondence to Yu Fu.

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Fu, Y. Biharmonic Submanifolds with Parallel Mean Curvature Vector in Pseudo-Euclidean Spaces. Math Phys Anal Geom 16, 331–344 (2013). https://doi.org/10.1007/s11040-013-9134-1

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  • DOI: https://doi.org/10.1007/s11040-013-9134-1

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