A study on generalized Ricci 2-recurrent spaces. (English) Zbl 0948.53010

De, C. U.; Bandyopadhyay

Mat. Vesn. 50, No. 1-2, 47-52 (1998).

Let \(V_n\) be a Riemannian space with non-zero Ricci tensor \(R_{ij}\). This space is called a generalized Ricci 2-recurrent space if \(R_{ij}\) satisfies \(R_{ij,lm}=\lambda _m R_{ij,l} + a_{lm} R_{ij} , \) where \(a_{lm}\) is non-zero and the comma denotes covariant differentiation with respect to the metric tensor \(g_{ij}\). The main purpose of this paper is to study some properties of a generalized Ricci 2-recurrent space, as well as to construct an example.

Reviewer: Neda Bokan (Novi Beograd)

MSC:

53B20

Local Riemannian geometry

Keywords:

recurrent space; generalized Ricci recurrent space; Ricci principle