Study on Einstein-K ̈aehlerian Decomposable Recurrent Space of First Order

K S Rawat; Sandeep Chauhan

doi:10.56424/jts.v9i01.10567

K S Rawat Department of Mathematics H.N.B. Garhwal University Campus, Badshahi Thaul, Tehri (Garhwal) -249199 (Uttarakhand), India
Sandeep Chauhan Department of Mathematics H.N.B. Garhwal University Campus, Badshahi Thaul, Tehri (Garhwal) -249199 (Uttarakhand), India

DOI: https://doi.org/10.56424/jts.v9i01.10567

Keywords: K¨aehlerian space, Einstein space, Einstein K¨aehlerian space, recurrent space, Curvature tensor, Projective curvature tensor

Abstract

Takano [2] have studied decomposition of curvature tensor in a recurrent space. Sinha and Singh [3] have been studied and defined decomposition of recurrent curvature tensor field in a Finsler space. Singh and Negi studied decomposition of recurrent curvature tensor field in a K¨aehlerian space. Negi and Rawat [6] have studied decomposition of recurrent curvature tensor field in K¨aehlerian space. Rawat and Silswal [11] studied and defined decomposition of recurrent curvature tensor fields in a Tachibana space. Further, Rawat and Kunwar Singh [12] studied the decomposition of curvature tensor field in K¨aehlerian recurrent space of first order. In the present paper, we have studied the decomposition of curvature tensor fields R^h_ijk in terms of two non-zero vectors and a tensor field in EinsteinK¨aehlerian recurrent space of first order and several theorem have been established and proved.