On Einstein warped product space with respect to semi symmetric metric connection

Year 2021, Volume: 50 Issue: 5, 1477 - 1490, 15.10.2021

Buddhadev Pal , Pankaj Kumar

https://doi.org/10.15672/hujms.755030

Abstract

In this paper, we study Einstein warped product space with respect to semi symmetric metric connection. During this study we establish some results on curvature, Ricci and scalar tensors with respect to semi symmetric metric connection and second order semi symmetric metric connection. In the last section, we investigate under what conditions, if $M$ is an Einstein warped space with nonpositive scalar curvature and compact base with respect to semi symmetric metric connection then $M$ is simply a Riemannian product space.

Keywords

Einstein manifold, semi symmetric metric connection, Warped product space, Ricci tensor, Hessian tensor, Ricci identity

Thanks

The Second author is supported by UGC JRF of India, Ref. No: 1269/(SC)(CSIR-UGC NET DEC. 2016).

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