A study on generalized Ricci 2-recurrent spaces

Abstract

The object of the present paper is to study some properties of generalized Ricci 2-recurrent spaces. At first it is proved that every 3-dimensional generalized Ricci 2-recurrent space is a generalized 2-recurrent space. In section 3, it is shown that for such a space Ricci-principal invariant is $1/2R$. In section 4 we find a necessary condition for such a space to be a Ricci-recurrent space. Next it is proved that a conformally symmetric Ricci 2-recurrent space is a generalized 2-recurrent space and a conformally symmetric generalized Ricci 2-recurrent space with definite metric and zero scalar curvature can not exist. Lastly an example of a generalized Ricci 2-recurrent space is also constructed.