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Geometry of Finsler subspaces. I. (English) Zbl 0622.53018
Finsler subspaces \(F^ m\) of a Finsler space \(F^ n\) were studied by many geometers: E. Cartan, M. Haimovici, E. T. Davies, M. Matsumoto etc. The reviewer and the author [ibid. 30, No.4, 56-59 (1984; Zbl 0577.53029)], have given a complete description of these spaces in the case when \(F^ m\) has the so-called ”property of horizontality”.
In the present paper the author extends this study to the general case using an arbitrary Finsler connection in \(F^ n\) and the induced Finsler connections on some vector bundles associated to \(F^ m\) in \(F^ n\). The Gauss-Weingarten formulas and Gauss-Codazzi equations for Finsler subspaces \(F^ m\) in a Finsler space \(F^ n\) are established.
Reviewer: R.Miron

53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)
Zbl 0577.53029