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Symmetry 2019, 11(2), 200; https://doi.org/10.3390/sym11020200

Chen Inequalities for Warped Product Pointwise Bi-Slant Submanifolds of Complex Space Forms and Its Applications

Department of Mathematics, College of Science, King Khalid University, 9004 Abha, Saudi Arabia
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Received: 24 December 2018 / Revised: 23 January 2019 / Accepted: 31 January 2019 / Published: 11 February 2019
(This article belongs to the Special Issue Geometry of Submanifolds and Homogeneous Spaces)
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Abstract

In this paper, by using new-concept pointwise bi-slant immersions, we derive a fundamental inequality theorem for the squared norm of the mean curvature via isometric warped-product pointwise bi-slant immersions into complex space forms, involving the constant holomorphic sectional curvature c, the Laplacian of the well-defined warping function, the squared norm of the warping function, and pointwise slant functions. Some applications are also given. View Full-Text
Keywords: mean curvature; warped products; compact Riemannian manifolds; pointwise bi-slant immersions; inequalities mean curvature; warped products; compact Riemannian manifolds; pointwise bi-slant immersions; inequalities
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Ali, A.; Alkhaldi, A.H. Chen Inequalities for Warped Product Pointwise Bi-Slant Submanifolds of Complex Space Forms and Its Applications. Symmetry 2019, 11, 200.

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