Indian Journal of Science and Technology

Abstract

Objectives: The purpose of this paper is to obtain several results in the field of generalised neo-pseudo projective recurrent Finsler space. Methods: A generalization technique is employed to solve the resulting problem. We provide its application in the study of space-time. Findings: In section 1, we have defined and studied some of the basic and useful results for later work. Section 2 deals for the neo-pseudo projective recurrent curvature tensor. The notion of neo-pseudo projective recurrent space of second order has been delineated in the section 3. In the section 4 we have studied the generalised neo-pseudo projective recurrent space and established several new results. Novelty/Conclusion: In this paper we have studied some recurrent properties of neo-pseudo projective curvature tensor in a Finsler space. We have obtained several new results which are as follows:
• If the space Fn admits a neo-pseudo projective curvature tensor Qa bgd then Qa bgd is skew-symmetric with regard to last two indices.
• If the neo-pseudo projective deviation tensor Qab and pseudo deviation tensor field Tab coincides to each other for q = 1 then space is W-flat.
• If Fn admits the projectively flat Q-recurrent space then the relation
ÑeQa
bg +ÑbQa
ge +ÑgQa
eb = 0 holds good.
• If a Finsler space Fn admits projectively flat Q-birecurrent space then the relation KerQa
bg +KbrQa
ge +KgrQa
eb = 0 holds good.
• If the space is Q-birecurrent then the generalised Q-recurrent space is Qsymmetric.
• For the projective flat generalised Q-recurrent space the relation
ÑrÑeQa
gd +ÑrÑgQa
de +ÑrÑdQa
eg = 0 holds good.
AMS Subject Classification: 58B20, 53C20, 53C60.