Parabolicity of minimal graphs in Riemannian warped products and rigidity theorems

An elementary probabilistic argument is presented which shows that for every forest $F$ other than a matching, and every graph $G$ containing a cycle, there exists an infinite number of graphs $J$ such that $J\to (F,G)$ but if we delete from $J$ any edge $e$ the graph $J-e$ obtained in this way does not have this property.

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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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