Doubly Warped Product Submanifolds of a Riemannian Manifold of Nearly Quasi-constant Curvature
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Abstract
In the present paper, we form a sharp inequality for a doubly warped product submanifold of a Riemannian manifold of nearly quasi-constant curvature.
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References
J. Beem, P. Ehrlich and T. G. Powell, Warped product manifolds in relativity, Selected Studies: A volume dedicated to the memory of Albert Einstein (1982), 41–56.
J. K. Beem,Global lorentzian geometry, Routledge, 2017.
R. L. Bishop and B. O’Neill, Manifolds of negative curvature, Transactions of the American Mathematical Society 145 (1969), 1–49.
B. Y. Chen, Some pinching and classification theorems for minimal submanifolds, Archiv der Mathematik 60 (1993), 568–578.
B. Y. Chen, On isometric minimal immersions from warped products into real space forms, Proceedings of the Edinburgh Mathematical Society 45 (2002), 579–587.
B. Y. Chen, Differential geometry of warped product manifolds and submanifolds, World Scientific Singapore, 2017.
B. Y. Chen and K. Yano, Hypersurfaces of a conformally flat space, Tensor(NS) 26 (1972), 318–322.
A. K. Gazi and U. C. De On the existence of nearly quasi-Einstein manifolds, Novi Sad J. Math 39 (2009), 111–117.
S. W. Hawking and G. F. R. Ellis, The large scale structure of space- time, Vol. 1. Cambridge university press, 1973.
A. Olteanu, A general inequality for doubly warped product submanifolds, Mathematical Journal of Okayama University 52 (2010), 133-142.
S. Sular, Doubly warped product submanifolds of a Riemannian manifold of quasi-constant curvature, Annals of the Alexandru Ioan Cuza University- Mathematics 61 (2015), 235–244.
B. Unal, Doubly warped products [ph.d.thesis], University of Missouri Columbia(2000).