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Bernstein type properties of two-sided hypersurfaces immersed in a Killing warped product

Antonio W. Cunha, Eudes L. de Lima, Henrique F. de Lima, Eraldo A. Lima Jr., Adriano A. Medeiros (2016)

Studia Mathematica

Our purpose is to apply suitable maximum principles in order to obtain Bernstein type properties for two-sided hypersurfaces immersed with constant mean curvature in a Killing warped product M × ρ , whose curvature of the base Mⁿ satisfies certain constraints and whose warping function ρ is concave on Mⁿ. For this, we study situations in which these hypersurfaces are supposed to be either parabolic, stochastically complete or, in a more general setting, L¹-Liouville. Rigidity results related to entire...

Chen-Ricci inequalities for submanifolds of Riemannian and Kaehlerian product manifolds

Erol Kılıç, Mukut Mani Tripathi, Mehmet Gülbahar (2016)

Annales Polonici Mathematici

Some examples of slant submanifolds of almost product Riemannian manifolds are presented. The existence of a useful orthonormal basis in proper slant submanifolds of a Riemannian product manifold is proved. The sectional curvature, the Ricci curvature and the scalar curvature of submanifolds of locally product manifolds of almost constant curvature are obtained. Chen-Ricci inequalities involving the Ricci tensor and the squared mean curvature for submanifolds of locally product manifolds of almost...

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