<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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].</p></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].

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

College of Mathematics and Information Science Henan Normal University Xinxiang 453007, Henan,

School of Mathematical Sciences Dalian University of Technology Dalian 116024, Liaoning,

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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...

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

Published Online: Apr 22, 2017

Page range: 259 - 277

Received: May 01, 2013

Accepted: Sep 01, 2013

DOI: https://doi.org/10.1515/auom-2015-0041

Keywords
Complete spacelike hypersurface, semi-Riemannian warped product, r-th mean curvature, Bernstein-type theorem

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Published Online: Apr 22, 2017

Page range: 259 - 277

Received: May 01, 2013

Accepted: Sep 01, 2013

DOI: https://doi.org/10.1515/auom-2015-0041

KeywordsComplete spacelike hypersurface, semi-Riemannian warped product, r-th mean curvature, Bernstein-type theorem

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Complete spacelike hypersurface, semi-Riemannian warped product, r-th mean curvature, Bernstein-type theorem