Ricci curvature of semi-slant warped product submanifolds in generalized complex space forms

Ali H. Alkhaldi; Meraj Ali Khan; Shyamal Kumar Hui; Pradip Mandal; Ali H. Alkhaldi; Meraj Ali Khan; Shyamal Kumar Hui; Pradip Mandal

doi:10.3934/math.2022394

AIMS Mathematics

2022, Volume 7, Issue 4: 7069-7092. doi: 10.3934/math.2022394

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Research article

Ricci curvature of semi-slant warped product submanifolds in generalized complex space forms

1.
Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
2.
Computational and Analytical Mathematics and Their Applications Research Group, Department of Mathematics Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia
3.
Department of Mathematics, The University of Burdwan, Burdwan-713104, West Bengal, India

Received: 19 July 2021 Revised: 24 January 2022 Accepted: 26 January 2022 Published: 08 February 2022
MSC : 53C25, 53C40, 53C42, 53D15

The objective of this paper is to achieve the inequality for Ricci curvature of a semi-slant warped product submanifold isometrically immersed in a generalized complex space form admitting a nearly Kaehler structure in the expressions of the squared norm of mean curvature vector and warping function. In addition, the equality case is likewise discussed. We provide numerous physical applications of the derived inequalities. Later, we proved that under a certain condition the base manifold $ N_T^{n_1} $ is isometric to a $ n_1 $-dimensional sphere $ S^{n_1}(\frac{\lambda_1}{n_1}) $ with constant sectional curvature $ \frac{\lambda_1}{n_1}. $
- Ricci curvature,
- Laplacian,
- Hamiltonian,
- Dirichlet energy
Citation: Ali H. Alkhaldi, Meraj Ali Khan, Shyamal Kumar Hui, Pradip Mandal. Ricci curvature of semi-slant warped product submanifolds in generalized complex space forms[J]. AIMS Mathematics, 2022, 7(4): 7069-7092. doi: 10.3934/math.2022394

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Abstract

The objective of this paper is to achieve the inequality for Ricci curvature of a semi-slant warped product submanifold isometrically immersed in a generalized complex space form admitting a nearly Kaehler structure in the expressions of the squared norm of mean curvature vector and warping function. In addition, the equality case is likewise discussed. We provide numerous physical applications of the derived inequalities. Later, we proved that under a certain condition the base manifold $ N_T^{n_1} $ is isometric to a $ n_1 $-dimensional sphere $ S^{n_1}(\frac{\lambda_1}{n_1}) $ with constant sectional curvature $ \frac{\lambda_1}{n_1}. $

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