A class of indefinite almost paracontact metric manifolds

Authors

Keywords:

indefinite almost paracontact metric manifold, Ricci semi-symmetric manifold, (ϵ)-para Kenmotsu manifold, semi-symmetric and η- Einstein manifolds

Abstract

This research, we develop a new class of indefinite almost paracontact metric manifolds, termed ($\epsilon$)-para Kenmotsu manifolds and we obtain some typical identities for the curvature tensor, scalar curvature and Ricci tensor. Furthermore, in particular, we investigate the curvature features of $three$-dimensional ($\epsilon$)-para Kenmotsu manifolds. We establish an essential as well as sufficient condition for an ($\epsilon$)-para Kenmotsu $3$-manifold to have an indefinite space form. Furthermore, we classify and demonstrate that ($\epsilon$)-para Kenmotsu $3$-manifolds, which are either semi-symmetric, Ricci-semi-symmetric or semi-symmetric type, are $\eta$-Einstein. In conclusion, we create a $3$-D ($\epsilon$)-para Kenmotsu manifold example.

Author Biography

Sunitha Devi, Koneru Lakshmaiah Education Foundation

Professor, Department of Mathematics.

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Published

2025-03-23

How to Cite

S, S. D., & Prasad, K. L. S. . (2025). A class of indefinite almost paracontact metric manifolds. International Journal of Maps in Mathematics, 8(1), 247–257. Retrieved from https://simadp.com/journalmim/article/view/225