On Einstein–Sasakian holomorphically conformal bi-recurrent and bi- symmetric spaces

Abstract

Tachibana (1967), studied on the Bochner curvature tensor. Sinha and Singh (1971), studied on Kaehlerian spaces with recurrent Bochner curvature. Singh (1973), studied on a Kaehlerian space with recurrent holomorphic projective curvature tensor. Singh (1979), studied on Einstein – Kaehlerian Conharmonic recurrent space. Negi and Rawat (1997) studied theorems on Kaehlerian spaces with recurrent and symmetric Bochner curvature tensor. Rawat and Prasad (2008), studied and defined some recurrent and symmetric properties in an almost Kaehlerian space. Rawat and Uniyal (2010), studied on infinitesimal conformal and projective transformations of K-space and Kaehlerian recurrent space. Further, Rawat, Kumar and Uniyal (2012), studied on hyperbolically Kaehlerian bi-recurrent and bi-symmetric spaces. In the present paper, we have studied on Einstein- Sasakian holomorphically conformal bi-recurrent and bi-symmetric spaces and several theorems have been established and proved therein. The necessary and sufficient condition for an Einstein Sasakian space to be Einstein-Sasakian bi-recurrent and bi-symmetric has been investigated.