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On Finsler-Weyl manifolds and connections

Kozma, L. — 1996

Proceedings of the 15th Winter School "Geometry and Physics"

Let $M$ be a manifold with all structures smooth which admits a metric $g$ . Let $Γ$ be a linear connection on $M$ such that the associated covariant derivative $\nabla$ satisfies $\nabla g = g \otimes w$ for some 1-form $w$ on $M$ . Then one refers to the above setup as a Weyl structure on $M$ and says that the pair $(g, w)$ fits $Γ$ . If $σ : M \to ℝ$ and if $(g, w)$ fits $Γ$ , then $(e^{σ g}, w + d σ)$ fits $Γ$ . Thus if one thinks of this as a map $g \mapsto w$ , then $e^{σ g} \mapsto w + d σ$ .In this paper, the author attempts to apply Weyl’s idea above to Finsler spaces. A Finsler fundamental function $L : T M \to ℝ$ satisfies (i) $L (u) > 0$ for...

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