2012/02/28 by Mukut Mani Tripathi, Punam Gupta, Tripathi, Mukut Mani +1 · 1 citation
Mathematics · Physics and Astronomy · #53C25 #53C50 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities #math.DG #msc:53C25 #msc:53C50
paper · pdf · doi:10.48550/arxiv.1202.6138
arxiv created 2012/02/28 · openalex publication_date 2012/02/28 · arxiv updated 2012/02/29 · openalex created_date 2021/04/26 · openalex updated_date 2026/07/28
(N(k),ξ)-semi-Riemannian manifolds are defined. Examples and properties of (N(k),ξ)-semi-Riemannian manifolds are given. Some relations involving \cal Ta-curvature tensor in (N(k),ξ)-semi-Riemannian manifolds are proved. ξ-\cal Ta-flat (N(k),ξ)-semi-Riemannian manifolds are defined. It is proved that if M is an n-dimensional ξ-\cal Ta-flat (N(k),ξ)-semi-Riemannian manifold, then it is η-Einstein under an algebraic condition. We prove that a semi-Riemannian manifold, which is T-recurrent or T-symmetric, is always T-semisymmetric, where T is any tensor of type (1,3). (\cal Ta, \cal Tb) -semisymmetric semi-Riemannian manifold is defined and studied. The results for \cal Ta-semisymmetric, \cal Ta-symmetric, \cal Ta-recurrent (N(k),ξ)-semi-Riemannian manifolds are obtained. The definition of (\cal Ta,S_\cal Tb)-semisymmetric semi-Riemannian manifold is given. (\cal Ta,S_\cal Tb)-semisymmetric (N(k),ξ)-semi-Riemannian manifolds are classified. Some results for \cal Ta-Ricci-semisymmetric (N(k),ξ)-semi-Riemannian manifolds are obtained.