A Class of Riemannian Manifolds with Special Form of Curvature Tensor
Musa A. A. Jawarneh *
University of Jeddah, Al-Kamil Faculty of Science and Arts, Department of mathematics, P.O.Box 110, Alkamil 21931, Al-Kamil, Saudi Arabia.
*Author to whom correspondence should be addressed.
Abstract
Riemannian curvature is determined by the Ricci curvature by a special formula to introduce a special class of Riemannian manifolds which called Jawarneh manifold. Some geometric properties of Jawarneh manifold have been derived and a non-trivial example is obtained to prove the existence.
Keywords: Riemannian manifold, flat manifold, Einstein manifold, symmetric manifold, Ricci symmetric manifold, conformally flat manifold, cosmology.