2012/02/29 by Mukut Mani Tripathi, Punam Gupta, Tripathi, Mukut Mani +1
Mathematics · #53C25 #53C50 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C25 #msc:53C50
paper · pdf · doi:10.48550/arxiv.1202.6458
arXiv admin note: text overlap with arXiv:1202.6138
arxiv created 2012/02/29 · arxiv updated 2012/03/19
Definition of (\cal Ta,\cal Tb)-pseudosymmetric semi-Riemannian manifold is given. (\cal Ta,\cal Tb)-pseudosy mmetric (N(k),ξ)-semi-Riemannian manifolds are classified. Some results for \cal Ta-pseudosymmetric (N(k),ξ)-semi-Riemannian manifolds are obtained. (\cal Ta,\cal Tb,Sℓ)-pseudosymmetric semi-Riemannian manifolds are defined. (\cal Ta,\cal Tb,Sℓ)-pseudosymmetric (N(k),ξ)-semi-Riemannian manifolds are classified. Some results for (R,\cal Ta,Sℓ)-pseudosymmetric (N(k),ξ)-semi-Riemannian manifolds are obtained. In particular, some results for (R,\cal Ta,S)-pseudosymmetric (N(k),ξ)-semi-Riemannian manifolds are also obtained. After that, the definition of (\cal Ta,S_\cal Tb)-pseudosymmetric semi-Riemannian manifold is given. (\cal Ta,S_\cal Tb)-pseudosymmetric (N(k),ξ)-semi-Riemannian manifolds are classified. It is proved that a (R,S_\cal Ta)-pseudosymmetric (N(k),ξ)-semi-Riemannian manifold is either Einstein or L=k under an algebraic condition. Some results for (\cal Ta,S)-pseudosymmetric (N(k),ξ)-semi-Riemannian manifolds are also obtained. In last, (\cal Ta,S_\cal Tb,Sℓ)-pseudosymmetric semi-Riemannian manifolds are defined and (\cal Ta,S_\cal Tb,Sℓ) -pseudosymmetric (N(k),ξ)-semi-Riemannian manifolds are classified.