Research Article

Some geometric and physical properties of pseudo ψ-conharmonically symmetric manifolds

Published in: Quaestiones Mathematicae
Volume 46 , issue 5 , 2023 , pages: 939–958

DOI: 10.2989/16073606.2022.2046197

Author(s): Krishnendu De Kabi Sukanta Mahavidyalaya, The University of Burdwan, India , Uday Chand De University of Calcutta, India

Keywords: 53B30 , 53B50 , 53C15 , 53C50 , ψ-conharmonic curvature tensor , pseudo ψ-conharmonically symmetric manifolds ,

spacetime

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Abstract

In this article, we present a new tensor that generalizes the conharmonic curvature tensor, termed the ψ-conharmonic curvature tensor. In the first part, we derive some fundamental geometrical properties of a pseudo ψ-conharmonically symmetric manifold (briefly, ) and give some fascinating outcomes. Among others, we establish that an Einstein manifold is of zero scalar curvature. Besides, we investigate ψ-conharmonically flat perfect fluid and spacetimes, respectively. As a result, we acquire some significant theorems. Finally, we construct several non-trivial examples to establish the existence of .

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