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Volume 7
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Article

The First Eigenvalue Estimates of Warped Product Pseudo-Slant Submanifolds

by
Rifaqat Ali
1,
Ali H. Alkhaldi
1,
Akram Ali
1 and
Wan Ainun Mior Othman
2,*
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.
Mathematics 2019, 7(2), 162; https://doi.org/10.3390/math7020162
Submission received: 13 January 2019 / Revised: 1 February 2019 / Accepted: 7 February 2019 / Published: 11 February 2019
Versions Notes

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.
Keywords: nearly cosymplectic manifold; warped products; pseudo-slant; inequality; eigenvalue nearly cosymplectic manifold; warped products; pseudo-slant; inequality; eigenvalue

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MDPI and ACS Style

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. https://doi.org/10.3390/math7020162

AMA Style

Ali R, Alkhaldi AH, Ali A, Othman WAM. The First Eigenvalue Estimates of Warped Product Pseudo-Slant Submanifolds. Mathematics. 2019; 7(2):162. https://doi.org/10.3390/math7020162

Chicago/Turabian Style

Ali, Rifaqat, Ali H. Alkhaldi, Akram Ali, and Wan Ainun Mior Othman. 2019. "The First Eigenvalue Estimates of Warped Product Pseudo-Slant Submanifolds" Mathematics 7, no. 2: 162. https://doi.org/10.3390/math7020162

APA Style

Ali, R., Alkhaldi, A. H., Ali, A., & Othman, W. A. M. (2019). The First Eigenvalue Estimates of Warped Product Pseudo-Slant Submanifolds. Mathematics, 7(2), 162. https://doi.org/10.3390/math7020162

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