Author/Authors :
Shaikh ، A.A. - University of Burdwan , Roy ، I. - University of Burdwan , Kundu ، H. - University of Burdwan
Abstract :
The object of the present paper is to introduce and study a type of non-flat semi-Riemannian manifolds, called, super generalized recurrent manifolds which generalizes both the notion of hyper generalized recurrent manifolds [A.A. Shaikh and A. Patra, On a generalized class of recurrent manifolds, Arch. Math. (Brno) 46 (2010) 71--78.] and weakly generalized recurrent manifolds [A.A. Shaikh and I. Roy, On weakly generalized recurrent manifolds, Ann. Univ. Sci. Budapest Rolando Eotvos, Sect. Math. 54 (2011) 35--45.]. The nature of associated 1-forms of a super generalized recurrent manifold is determined and it is proved that on a Roter type manifold [R. Deszcz, On Roter type manifolds, in: 5th Conference on Geometry and Topology of Manifolds, Krynica, Poland, 2003.] such a notion is equivalent to the notion of generalized Ricci-recurrent manifold [U.C. De, N. Guha and D. Kamilya, On generalized Ricci-recurrent manifolds, Tensor (N.S.) 56 (1995), no. 3, 312--317.]. We also obtain a sufficient condition for a super generalized recurrent manifold to be a semisymmetric one and the existence of such notion is ensured by a proper example.
Keywords :
Recurrent manifold , hyper generalized recurrent manifold , weakly generalized recurrent manifold , super generalized recurrent manifold , semisymmetric manifold , Roter type manifold
