W8 - Curvature Tensor in Generalized Sasakian Space Forms

Authors

  • Gyanvendra Pratap Singh Department of Mathematics and Statistics Deen Dayal Upadhyaya Gorakhpur University Gorakhpur-273009 (UP) INDIA.
  • R Rajan Department of Mathematics and Statistics Deen Dayal Upadhyaya Gorakhpur University Gorakhpur-273009 (UP) INDIA.
  • Anand Kumar Mishra Department of Mathematics and Statistics Deen Dayal Upadhyaya Gorakhpur University Gorakhpur-273009 (UP) INDIA.
  • Pawan Prajapati Department of Mathematics and Statistics Deen Dayal Upadhyaya Gorakhpur University Gorakhpur-273009 (UP) INDIA.

DOI:

https://doi.org/10.23755/rm.v48i0.961

Keywords:

Sasakian space form, generalized Sasakian space form, ϕ−recurrent, ϕ-symmetric, ϕ-semisymmetric, W8- curvature tensor, Einstein manifold, η-Einstein manifold.

Abstract

The generalized Sasakian-space-forms and their properties have been examined by various researchers such as Alegre and Carriazo [2008], Prakasha [2012], Sarkar and Akbar [2014], Shanmukha et al. [2018], Sarkar and Sen [2012], Rajan and Singh [2020] and Sarkar and Sen [2012]. Motivated by the results of these works, we have proposed the idea of the W8−curvature tensor in generalized Sasakian-space- forms. The main goal of this paper is to investigate the curvature properties of generalized Sasakian-space-forms that satisfy the conditions ξ − W8− flatness, ϕ − W8−semi-symmetric, W8 · Q = 0, W8 · R = 0 and to prove some interesting results.

Author Biographies

  • Gyanvendra Pratap Singh, Department of Mathematics and Statistics Deen Dayal Upadhyaya Gorakhpur University Gorakhpur-273009 (UP) INDIA.
    Assistant Professor
  • R Rajan, Department of Mathematics and Statistics Deen Dayal Upadhyaya Gorakhpur University Gorakhpur-273009 (UP) INDIA.
    Research Scholar
  • Anand Kumar Mishra, Department of Mathematics and Statistics Deen Dayal Upadhyaya Gorakhpur University Gorakhpur-273009 (UP) INDIA.
    Research Scholar

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Published

2023-12-30

Issue

Vol. 48 (2023)

Section

Volume 48-2023

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