PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 61(75), pp. 9096 (1997) 

On a type of semisymmetric metric connection on a Riemannian manifoldU.C. De and S.C. BiswasAbstract: The properties of Riemannian manifolds admitting a semisymmetric metric connection were studied by many authors ([1], [2], [3], [4], [5], [6]). In [4] an expression of the curvature tensor of a manifold was obtained under assumption that the manifold admits a semisymmetric metric connection with vanishing curvature tensor and recurrent torsion tensor. Also in [7] Prvanovi\'c and Pusi\'c obtained an expression for curvature tensor of a Riemannian manifold, locally decomposable Riemannian space and the Kähler space which admits a semisymmetric metric connection $\tilde\nabla $ with vanishing curvature tensor and torsion tensor $T^h_{1m}$ satisfying $\tilde\nabla_k\tilde\nabla_j T^h_{1m}\tilde\nabla_j\tilde\nabla_k T^h_{1m} =0$. We study a type of semisymmetric metric connection $\tilde\nabla$ satisfying $\tilde R (X, Y)T=0$ and $\omega(\tilde R(X,Y)Z)=0$, where $T$ is the torsion tensor of the semisymmetric connection, $\tilde R$ is the curvature tensor corresponding to $\tilde\nabla$ and $\omega$ is the associated 1form of $T$. Classification (MSC2000): 53C05 Full text of the article:
Electronic fulltext finalized on: 1 Nov 2001. This page was last modified: 6 Feb 2002.
© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
