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Special Finsler spaces admitting a semi-concurrent vector field

M. R. Rajeshwari, S. K. Narasimhamurthy, H. M. Manjunatha

Abstract

The main objective of this paper is to study semi-concurrent vector fields on a Finsler manifold. We show that the quasi-$C$-reducible Finsler space, $C3$-like Finsler space, $C^{h}$-recurrent Finsler space, and $P2$-like Finsler space are equivalent to Riemannian if they admit a semi-concurrent vector field. Further, we prove the necessary and sufficient condition for a Finsler space satisfying $C$-conformal condition to become Riemannian.

Special Finsler spaces admitting a semi-concurrent vector field

Abstract

The main objective of this paper is to study semi-concurrent vector fields on a Finsler manifold. We show that the quasi--reducible Finsler space, -like Finsler space, -recurrent Finsler space, and -like Finsler space are equivalent to Riemannian if they admit a semi-concurrent vector field. Further, we prove the necessary and sufficient condition for a Finsler space satisfying -conformal condition to become Riemannian.

Paper Structure

This paper contains 4 sections, 8 theorems, 49 equations.

Table of Contents

  1. Introduction
  2. Notations and preliminaries
  3. Semi-concurrent vector fields
  4. Conclusions

Key Result

Lemma 1

e19 For the nonzero function $B^i$ satisfying e:e25, if the scalars $\alpha$ and $\alpha'$ satisfy then $\alpha = \alpha' = 0$, which means that the two vector fields $B^i(x)$ and $y^i$ are independent.

Theorems & Definitions (27)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Definition 7
  • Definition 8
  • Definition 9
  • Definition 10
  • ...and 17 more