Warped products admitting a curvature bound

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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Harmonic branched coverings and uniformization of CAT(k) spheres

Journal für die reine und angewandte Mathematik (Crelles Journal) ◽

10.1515/crelle-2021-0031 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Christine Breiner ◽

Chikako Mese

Keyword(s):

Harmonic Map ◽

Branched Coverings ◽

Curvature Bound ◽

Branched Covering

Abstract Let S be a surface with a metric d satisfying an upper curvature bound in the sense of Alexandrov (i.e. via triangle comparison). We show that an almost conformal harmonic map from a surface into ( S , d ) {(S,d)} is a branched covering. As a consequence, if ( S , d ) {(S,d)} is homeomorphically equivalent to the 2-sphere 𝕊 2 {\mathbb{S}^{2}} , then it is conformally equivalent to 𝕊 2 {\mathbb{S}^{2}} .

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Curvature bound for a curve flow with a prescribed rate of change in enclosed area

International Journal of Mathematics ◽

10.1142/s0129167x18500532 ◽

2018 ◽

Vol 29 (08) ◽

pp. 1850053

Author(s):

Jianbo Fang ◽

Shengliang Pan ◽

Yunlong Yang

Keyword(s):

Rate Of Change ◽

Partial Answer ◽

Curvature Bound ◽

Curve Flow ◽

Nonlocal Flow

This paper deals with the curvature bound for a nonlocal curve flow with a prescribed rate of change in enclosed area via Andrews–Bryan’s distance comparison. As a by-product, a partial answer to a conjecture given by Dallaston and McCue is obtained and the [Formula: see text] convergence of the curvature for the nonlocal flow is achieved.

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