Study on a Class of P-Kenmotsu Manifolds Admitting Weyl-projective Curvature Tensor of Type (1, 3) | Chapter 3 | Recent Advances in Mathematical Research and Computer Science Vol. 1

We investigated a class of para-Kenmotsu manifolds that admit the type Weyl-projective curvature tensor (1, 3). The following is a breakdown of the current project: Section 2 contains certain prerequisites related to P-Kenmotsu manifolds. We describe W2-recurrent and semisymmetric para-Kenmotsu manifolds in Section 3 and prove that the W2-recurrent para-Kenmotsu manifold is semisymmetric. Finally, an n-dimensional (n > 2) P-Kenmotsu manifold is proved to be Ricci semisymmetric only if and only if it is an Einstein manifold.

Author (S) Details

K. L. Sai Prasad
Department of Mathematics, Gayatri Vidya Parishad College of Engineering for Women, Visakhapatnam, India.

S. Sunitha Devi
Department of Mathematics, Vignan Institute of Information Technology, Visakhapatnam, India.

G. V. S. R. Deekshitulu
Department of Mathematics, Jawaharlal Nehru Technological University, Kakinada, India.

View Book :- https://stm.bookpi.org/RAMRCS-V1/article/view/4333

Studies on a Type of Para-Kenmotsu Manifold | Chapter 9 | Current Topics on Mathematics and Computer Science Vol. 9

We look at a class of virtually para-contact metric manifolds called para-Kenmotsu (or P-Kenmotsu) manifolds Mn that admit the condition R in this chapter (X, Y). C = 0, where C denotes the manifold's conformal curvature tensor and R denotes the Riemannian curvature tensor. For tangent vectors X and Y, R(X, Y) is a derivation of the tensor algebra at each point of the manifold. We investigate and demonstrate that a P-Kenmotsu manifold (Mn, g) (n > 3) admitting the condition R is a P-Kenmotsu manifold (Mn, g) (n > 3) (X, Y). C = 0 is conformally flat, hence it's an SP-Kenmotsu manifold, with Riemannian metric g. We have and hence for such a manifold R for a conformally symmetric Riemannian manifold (X, Y). C = 0 is valid. As a result, we can deduce the following conclusion. An SP-Kenmotsu manifold is a conformally symmetric P-Kenmotsu manifold (Mn, g) (n > 3). The chapter concludes with a statement that the physical relevance of the structures and relationships presented in this chapter should be identified and strengthened.

Author (S) Details

T. Satyanarayana

Department of Mathematics, Pragati Engineering College, Surampalem, Near Peddapuram, Andhra Pradesh, India.

K. L. Sai Prasad

Department of Mathematics, GVP College of Engineering For Women, Visakhapatnam, Andhra Pradesh, India.

View Book :- https://stm.bookpi.org/CTMCS-V9/article/view/3641