ON PARA-KENMOTSU MANIFOLDS ADMITTING ZAMKOVOY CONNECTION
By
Swati Jain1 , M. K. Pandey2 and A. Goyal3
1,2,3Department of Mathematics, University Institute of Technology, Rajiv Gandhi Proudyogiki Vishwavidyalaya, Bhopal, Madhya Predesh, India-462033
Email: swatijain2884@gmail.com, mkp apsu@rediffmail.com,anil goyal03@rediffmail.com
(Received: May 11, 2024; In format: June 07, 2024; Revised: October 08, 2024; Accepted: October 10, 2024)
DOI: https://doi.org/10.58250/jnanabha.2024.54215
Abstract
The goal of this paper is to study a PK-manifold (briefly, PK-manifold) that admits a Zamkovoy connection. We use a new (0, 2) type symmetric tensor Z to derive a new tensor field from the Mprojective curvature tensor (briefly, MP-curvature tensor). We call this new tensor field as generalised M-projective curvature tensor (briefly, GMP-curvature tensor). Further, we prove that a generalized M-projectively semi-symmetric PK-manifold turns out to be an Einstein manifold. Among others, it has been shown that the condition of generalized M-projectively φ-symmetry on PK-manifold admitting a Zamkovoy connection implies that the manifold is again an Einstein manifold.
2020 Mathematical Sciences Classification: 53C15, 53C25.
Keywords: M-projective and GMP-curvature tensors, PK-manifold, Zamkovoy connection, Einstein manifold.