<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Quasi-Einstein manifold and generalized quasi-Einstein manifold are the generalizations of Einstein manifold. The purpose of this paper is to study the mixed super quasi-Einstein manifold which is also the generalizations of Einstein manifold satisfying some curvature conditions. We define both Riemannian and Lorentzian doubly warped product on this manifold. Finally, we study the completeness properties of doubly warped products on <italic>MS</italic>(<italic>QE</italic>)<sub>4</sub> for both the Riemannian and Lorentzian cases.</p></abstract>

Quasi-Einstein manifold and generalized quasi-Einstein manifold are the generalizations of Einstein manifold. The purpose of this paper is to study the mixed super quasi-Einstein manifold which is also the generalizations of Einstein manifold satisfying some curvature conditions. We define both Riemannian and Lorentzian doubly warped product on this manifold. Finally, we study the completeness properties of doubly warped products on MS(QE)4 for both the Riemannian and Lorentzian cases.

On some classes of mixed-super quasi-Einstein manifolds

Department of Mathematics, Jadavpur University, India

Department of Mathematics, Institute of Science, Banaras Hindu University, India

Department of Mathematics, Jadavpur University, India.

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On some classes of mixed-super quasi-Einstein manifolds"}

Quasi-Einstein manifold and generalized quasi-Einstein manifold are the generalizations of Einstein manifold. The purpose of this paper is to study the mixed...

On some classes of mixed-super quasi-Einstein manifolds

Published Online: Aug 02, 2016

Page range: 32 - 52

Received: Oct 12, 2015

DOI: https://doi.org/10.1515/ausm-2016-0003

Keywords
mixed super quasi-Einstein manifold, Ricci-pseudosymmetric manifold, Ricci semisymmetric manifold, concircular curvature tensor, quasi-conformal curvature tensor, warped product, doubly warped product

© 2016 Santu Dey et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On some classes of mixed-super quasi-Einstein manifolds

Published Online: Aug 02, 2016

Page range: 32 - 52

Received: Oct 12, 2015

DOI: https://doi.org/10.1515/ausm-2016-0003

Keywordsmixed super quasi-Einstein manifold, Ricci-pseudosymmetric manifold, Ricci semisymmetric manifold, concircular curvature tensor, quasi-conformal curvature tensor, warped product, doubly warped product

© 2016 Santu Dey et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
mixed super quasi-Einstein manifold, Ricci-pseudosymmetric manifold, Ricci semisymmetric manifold, concircular curvature tensor, quasi-conformal curvature tensor, warped product, doubly warped product