On the Action of W\(_i\) Curvature Tensors on Para-Sasakian Manifolds
Emel Karaca *
Department of Mathematics, Ankara Hacı Bayram Veli University, Ankara, Turkey.
Tugba Mert
Department of Mathematics, Sivas Cumhuriyet University, Sivas, Turkey.
Mehmet Atceken
Department of of Mathematics, Aksaray University, Aksaray, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this study, Riemann, Ricci, W6−, W7−, W8−, and W9− curvature tensors on para-Sasakian manifolds are examined. Our goal is to ascertain the connections among these tensors and the specific conditions in which being Einstein and η− Einstein manifolds emerge. The semisymmetric condition of W6 and the tensor products of W8 and W9 and W7 and W9 satisfy the condition of being an η− Einstein manifold, while the semisymmetric conditions of W7 and W9, the curvature conditions W6 ·R and W7 ·R, and the tensor product of W7 and W8 satisfy the condition of being an Einstein manifold.
Keywords: Para-sasakian manifold, einstein manifold, η− einstein manifold, curvature tensors