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On \(\mathcal C\)-conformal changes of Riemann-Finsler metrics. (English) Zbl 0966.53051

Slovák, Jan (ed.) et al., Proceedings of the 18th winter school “Geometry and physics”, Srní, Czech Republic, January 10-17, 1998. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 59, 221-228 (1999).
In this paper the author studies a coordinate free characterization of the \(C\)-conformality introduced by M. Hashiguchi. He proves that if \(\overline g=\varphi g\) is a \(C\)-conformal change of a Riemann-Finsler metric \(g\) on a two-dimensional manifold \(M\) with \(\text{grad} \varphi(v)\neq 0)\) \((v\in TM)\), then there is a connected neighborhood \(U\) of \(\pi(v)\) such that \((U,g/TU)\) is Riemannian manifold.
For the entire collection see [Zbl 0913.00039].

MSC:

53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
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