AIMS Mathematics (Jun 2021)

Biharmonic submanifolds of Kaehler product manifolds

  • Yanlin Li,
  • Mehraj Ahmad Lone,
  • Umair Ali Wani

DOI
https://doi.org/10.3934/math.2021541
Journal volume & issue
Vol. 6, no. 9
pp. 9309 – 9321

Abstract

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In this paper, the authors have established the necessary and sufficient conditions for the submanifolds of Kaehler product manifolds to be biharmonic. Moreover, the magnitude of scalar curvature for the hypersurfaces in a product of two unit spheres has been derived. Also, for the same product, the magnitude of the mean curvature vector for Lagrangian submanifolds has been estimated. Finally, the non-existence condition for totally complex Lagrangian submanifolds in a product of unit sphere and a hyperbolic space has been proved.

Keywords