Abstract
In this paper, we prove Chen’s general inequalities and Chen–Ricci inequalities for submanifolds of a Riemannian manifold of nearly quasi-constant curvature. We also establish inequalities between the warping function and the squared mean curvature for warped product submanifolds in a Riemannian manifold of nearly quasi-constant curvature.
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Acknowledgments
This paper was supported by the Foundation for Excellent Young Talents of Higher Education of Anhui Province (Grant no. 2011SQRL021ZD) and the Natural Science Foundation of Anhui Educational Committee (Grant no. KJ2010A125). The author would like to thank Professor Cihan Özgür for his kind help. The author would also like to take this opportunity to thank the referees for their corrections, helpful comments, and valuable suggestions for improving the manuscript.
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Zhang, P. Remarks on Chen’s Inequalities for Submanifolds of a Riemannian Manifold of Nearly Quasi-Constant Curvature. Vietnam J. Math. 43, 557–569 (2015). https://doi.org/10.1007/s10013-014-0096-9
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DOI: https://doi.org/10.1007/s10013-014-0096-9