Uniqueness of entire graphs in warped products

In this paper, we obtain new parametric uniqueness results for complete constant weighted mean curvature hypersurfaces under suitable geometric assumptions in weighted warped products. Furthermore, we also prove very general Bernstein type results for the constant mean curvature equation for entire graphs in these ambient spaces.

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Uniqueness of Complete Hypersurfaces in Weighted Riemannian Warped Products

Advances in Mathematical Physics ◽

10.1155/2021/3234263 ◽

2021 ◽

Vol 2021 ◽

pp. 1-9

Author(s):

Ning Zhang

Keyword(s):

Universal Covering ◽

Warped Products ◽

Bernstein Type ◽

Weighted Mean ◽

Weak Maximum Principle ◽

Uniqueness Results ◽

Weighted Mean Curvature ◽

Entire Graphs ◽

Special Case ◽

Complete Hypersurfaces

In this paper, applying the weak maximum principle, we obtain the uniqueness results for the hypersurfaces under suitable geometric restrictions on the weighted mean curvature immersed in a weighted Riemannian warped product I × ρ M f n whose fiber M has f -parabolic universal covering. Furthermore, applications to the weighted hyperbolic space are given. In particular, we also study the special case when the ambient space is weighted product space and provide some results by Bochner’s formula. As a consequence of this parametric study, we also establish Bernstein-type properties of the entire graphs in weighted Riemannian warped products.

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Curvature inequalities for C-totally real doubly warped products of locally conformal almost cosymplectic manifolds

Filomat ◽

10.2298/fil1720449a ◽

2017 ◽

Vol 31 (20) ◽

pp. 6449-6459 ◽

Cited By ~ 2

Author(s):

Akram Ali ◽

Siraj Uddin ◽

Wan Othman ◽

Cenap Ozel

Keyword(s):

Sectional Curvature ◽

Mean Curvature ◽

Warped Product ◽

Warped Products ◽

Equality Case ◽

Cosymplectic Manifolds ◽

Almost Cosymplectic Manifold ◽

Locally Conformal ◽

Totally Real ◽

Optimal Inequalities

In this paper, we establish some optimal inequalities for the squared mean curvature in terms warping functions of a C-totally real doubly warped product submanifold of a locally conformal almost cosymplectic manifold with a pointwise ?-sectional curvature c. The equality case in the statement of inequalities is also considered. Moreover, some applications of obtained results are derived.

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Pointwise pseudo-slant submanifolds of a Kenmotsu manifold

Filomat ◽

10.2298/fil1718833k ◽

2017 ◽

Vol 31 (18) ◽

pp. 5833-5853 ◽

Cited By ~ 1

Author(s):

Viqar Khan ◽

Mohammad Shuaib

Keyword(s):

Present Article ◽

Warped Product ◽

Shape Operator ◽

Warped Products ◽

Canonical Structure ◽

Slant Submanifold ◽

Kenmotsu Manifold ◽

Slant Submanifolds ◽

Kenmotsu Manifolds

In the present article, we have investigated pointwise pseudo-slant submanifolds of Kenmotsu manifolds and have sought conditions under which these submanifolds are warped products. To this end first, it is shown that these submanifolds can not be expressed as non-trivial doubly warped product submanifolds. However, as there exist non-trivial (single) warped product submanifolds of a Kenmotsu manifold, we have worked out characterizations in terms of a canonical structure T and the shape operator under which a pointwise pseudo slant submanifold of a Kenmotsu manifold reduces to a warped product submanifold.

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