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Mathematics 2019, 7(2), 162; https://doi.org/10.3390/math7020162

The First Eigenvalue Estimates of Warped Product Pseudo-Slant Submanifolds

1
Department of Mathematics, College of Science, King Khalid University, 9004 Abha, Saudi Arabia
2
Institute of Mathematical Sciences, University Malaya, Kuala Lumpur 50603, Malaysia
*
Author to whom correspondence should be addressed.
Received: 13 January 2019 / Revised: 1 February 2019 / Accepted: 7 February 2019 / Published: 11 February 2019
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Abstract

The aim of this paper is to construct a sharp general inequality for warped product pseudo-slant submanifold of the type M = M × f M θ , in a nearly cosymplectic manifold, in terms of the warping function and the symmetric bilinear form h which is known as the second fundamental form. The equality cases are also discussed. As its application, we establish a bound for the first non-zero eigenvalue of the warping function whose base manifold is compact. View Full-Text
Keywords: nearly cosymplectic manifold; warped products; pseudo-slant; inequality; eigenvalue nearly cosymplectic manifold; warped products; pseudo-slant; inequality; eigenvalue
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, R.; Alkhaldi, A.H.; Ali, A.; Othman, W.A.M. The First Eigenvalue Estimates of Warped Product Pseudo-Slant Submanifolds. Mathematics 2019, 7, 162.

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