scholarly journals Complete spacelike hypersurfaces with positive r-th mean curvature in a semi-Riemannian warped product

2015 ◽  
Vol 23 (2) ◽  
pp. 259-277
Author(s):  
Yaning Wang ◽  
Ximin Liu
Keyword(s):  
Sectional Curvature ◽  
Ricci Curvature ◽  
Curvature Tensor ◽  
Mean Curvature ◽  
Warped Product ◽  
Warped Products ◽  
Bernstein Type ◽  
Complete Spacelike Hypersurfaces ◽  
Spacelike Hypersurfaces ◽  
Comparison Inequality

Abstract In this paper, by supposing a natural comparison inequality on the positive r-th mean curvatures of the hypersurface, we obtain some new Bernstein-type theorems for complete spacelike hypersurfaces immersed in a semi-Riemannian warped product of constant sectional curvature. Generalizing the above results, under a restriction on the sectional curvature or the Ricci curvature tensor of the fiber of a warped product, we also prove some new rigidity theorems in semi-Riemannian warped products. Our main results extend some recent Bernstein-type theorems proved in [12, 13, 14].

scholarly journals On Bernstein-Type Theorems in Semi-Riemannian Warped Products

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Wenjie Wang ◽  
Ximin Liu
Keyword(s):  
Mean Curvature ◽  
Warped Products ◽  
Bernstein Type ◽  
Complete Spacelike Hypersurfaces ◽  
Spacelike Hypersurfaces ◽  
The Mean

Complete spacelike hypersurfaces immersed in semi-Riemannian warped products are investigated. By using a technique according to Yau (1976) and a reasonable restriction on the mean curvature of the hypersurfaces, we obtain some new Bernstein-type theorems which extend some known results proved by Camargo et al. (2011) and Colares and Lima (2012).

scholarly journals On Complete Spacelike Hypersurfaces in a Semi-Riemannian Warped Product

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Yaning Wang ◽  
Ximin Liu
Keyword(s):  
Hyperbolic Space ◽  
Mean Curvature ◽  
Warped Product ◽  
Constant Mean Curvature ◽  
Height Function ◽  
Bernstein Type ◽  
Complete Spacelike Hypersurfaces ◽  
Entire Vertical Graphs ◽  
Spacelike Hypersurfaces

By applying Omori-Yau maximal principal theory and supposing an appropriate restriction on the norm of gradient of height function, we obtain some new Bernstein-type theorems for complete spacelike hypersurfaces with nonpositive constant mean curvature immersed in a semi-Riemannian warped product. Furthermore, some applications of our main theorems for entire vertical graphs in Robertson-Walker spacetime and for hypersurfaces in hyperbolic space are given.

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

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6449-6459 ◽  
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.

scholarly journals Constant Mean Curvature Spacelike Surfaces in Lorentzian Warped Products

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Juan A. Aledo ◽  
Rafael M. Rubio
Keyword(s):  
Mean Curvature ◽  
Warped Product ◽  
Constant Mean Curvature ◽  
State Of The Art ◽  
The State ◽  
Warped Products ◽  
Type Result ◽  
Bernstein Type ◽  
Spacelike Surfaces ◽  
Lorentzian Warped Product

We characterize the spacelike slices of a Lorentzian warped product as the only constant mean curvature spacelike surfaces under suitable geometrical and physical assumptions. As a consequence of our study, we derive a Bernstein-type result which widely improves and extends the state-of-the-art results in this setting.

Complete spacelike hypersurfaces in a Robertson–Walker spacetime

2011 ◽  
Vol 151 (2) ◽  
pp. 271-282 ◽  
Author(s):  
ALMA L. ALBUJER ◽  
FERNANDA E. C. CAMARGO ◽  
HENRIQUE F. DE LIMA
Keyword(s):  
Maximum Principle ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Rigidity Results ◽  
Complete Spacelike Hypersurfaces ◽  
Uniqueness Results ◽  
Spacelike Hypersurfaces ◽  
Generalized Maximum Principle ◽  
Non Parametric

AbstractIn this paper, as a suitable application of the well-known generalized maximum principle of Omori–Yau, we obtain uniqueness results concerning to complete spacelike hypersurfaces with constant mean curvature immersed in a Robertson–Walker (RW) spacetime. As an application of such uniqueness results for the case of vertical graphs in a RW spacetime, we also get non-parametric rigidity results.

Exit radii of submanifolds from cylindrical domains in warped product manifolds

2015 ◽  
Vol 145 (3) ◽  
pp. 559-569
Author(s):  
Hironori Kumura
Keyword(s):  
Lower Bound ◽  
Bounded Domain ◽  
Ricci Curvature ◽  
Mean Curvature ◽  
Warped Product ◽  
Product Manifold ◽  
Warped Product Manifold ◽  
Cylindrical Domains ◽  
The Mean

Let UB(p0; ρ1) × f MV be a cylindrically bounded domain in a warped product manifold := MB × fMV and let M be an isometrically immersed submanifold in . The purpose of this paper is to provide explicit radii of the geodesic balls of M which first exit from UB(p0; ρ1) × fMV for the case in which the mean curvature of M is sufficiently small and the lower bound of the Ricci curvature of M does not diverge to –∞ too rapidly at infinity.

scholarly journals Spacelike hypersurfaces of constant mean curvature and Calabi-Bernstein type problems

1997 ◽  
Vol 49 (3) ◽  
pp. 337-345 ◽  
Author(s):  
Luis J. Alías ◽  
Alfonso Romero ◽  
Miguel Sánchez
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Bernstein Type ◽  
Spacelike Hypersurfaces

scholarly journals Biharmonic submanifolds in manifolds with bounded curvature

2016 ◽  
Vol 27 (11) ◽  
pp. 1650089
Author(s):  
Shun Maeta
Keyword(s):  
Riemannian Manifold ◽  
Sectional Curvature ◽  
Ricci Curvature ◽  
Mean Curvature ◽  
Biharmonic Submanifolds ◽  
Bounded Curvature ◽  
Negative Constant ◽  
The Mean ◽  
Biharmonic Submanifold

We consider a complete biharmonic submanifold [Formula: see text] in a Riemannian manifold with sectional curvature bounded from above by a non-negative constant [Formula: see text]. Assume that the mean curvature is bounded from below by [Formula: see text]. If (i) [Formula: see text], for some [Formula: see text], or (ii) the Ricci curvature of [Formula: see text] is bounded from below, then the mean curvature is [Formula: see text]. Furthermore, if [Formula: see text] is compact, then we obtain the same result without the assumption (i) or (ii). These are affirmative partial answers to Balmuş–Montaldo–Oniciuc conjecture.

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