Finsler cases of GF-space
Let \((M^{N-1}, r)\) be an \((N - 1)\)-dimensional Riemannian space. The author indicates a simple way of introducing the structure of generalized Finsler space over \(M^N =\mathbb{R} \times M^{N - 1}\) together with the associated tangent bundle \(TM\) of \(M^N\), and gives a simple condition that the space will be a Finsler space \(F^N\). The indicatrix of the space \(F^N\) \((N > 4)\) is a conformally flat space. The cases where the indicatrix is of constant curvature are investigated in detail, and a simple criterion for constancy of the indicatrix curvature is given (the analytical methods of introducing metric and connection over \(TM\) are applied). Note. The Finslerian solution for the static spherically symmetric gravitational field has been obtained by the author in Semin. Mec., Univ. Timişoara 25, 50 p. (1990; Zbl 0727.53034).
scientific article; zbMATH DE number 778307
scientific article