Characterization of Biharmonic Hypersurface

S.K. Srivastava; K. Sood; K. Srivastava

doi:10.15421/242211

Characterization of Biharmonic Hypersurface

S.K. Srivastava (Central University of Himachal Pradesh), https://orcid.org/0000-0001-5992-1902
K. Sood (Central University of Himachal Pradesh), https://orcid.org/0000-0001-8123-9002
K. Srivastava (Central University of Himachal Pradesh), https://orcid.org/0000-0003-2744-8406

Abstract

The main purpose of this paper is to study biharmonic hypersurface in a quasi-paraSasakian manifold $$$\mathbb{Q}^{2m+1}$$$. Biharmonic hypersurfaces are special cases of biharmonic maps and biharmonic maps are the critical points of the bienergy functional. The condition of biharmonicity for non-degenerate hypersurfaces in $$$\mathbb{Q}^{2m+1}$$$ is investigated for both cases: either the characteristic vector field of $$$\mathbb{Q}^{2m+1}$$$ is the unit normal vector field to the hypersurface or it belongs to the tangent space of the hypersurface. Some relevant examples are also illustrated.

Keywords

biharmonic map; biharmonic hypersurface; quasi-paraSasakian manifold

MSC 2020

53C25; 53C42; 53C50

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