Biharmonic submanifolds of Kaehler product manifolds

Yanlin Li; Mehraj Ahmad Lone; Umair Ali Wani; Yanlin Li; Mehraj Ahmad Lone; Umair Ali Wani

doi:10.3934/math.2021541

AIMS Mathematics

2021, Volume 6, Issue 9: 9309-9321. doi: 10.3934/math.2021541

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Research article

Biharmonic submanifolds of Kaehler product manifolds

1.
Department of Mathematics, Hangzhou Normal University, Hangzhou, 311121, China
2.
Department of Mathematics, NIT Srinagar, J & K, 190006, India

Received: 07 May 2021 Accepted: 08 June 2021 Published: 22 June 2021
MSC : 53C15, 53C40, 53C42, 53C43

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.
- biharmonic submanifolds,
- Kaehler product manifolds,
- totally real submanifolds,
- Lagrangian submanifolds,
- mean curvature
Citation: Yanlin Li, Mehraj Ahmad Lone, Umair Ali Wani. Biharmonic submanifolds of Kaehler product manifolds[J]. AIMS Mathematics, 2021, 6(9): 9309-9321. doi: 10.3934/math.2021541

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Abstract

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.

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