Beil metrics associated to a Finsler space. (English) Zbl 0916.53037

Section 1 consists of historical and bibliographical notes, and Section 2 states the geometrical language of the paper. The GL-metric is analysed in Section 3, formulating the conditions under which this metric is reduced to a Lagrange or a Finsler metric. Section 4 is dedicated to finding the connections that are compatible to a GL-metric. Some properties of parallel and concurrent Finsler vector fields are studied in Section 5. Then Section 6 refers to a GL-metric created by a concurrent Finsler vector field. Section 7 treats a Beil metric associated to a Finsler \((\alpha,\beta)\)-metric.


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