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On Bernstein type theorems in Finsler spaces with the volume form induced from the projective sphere bundle. (English) Zbl 1090.53061

The authors study Finsler minimal submanifolds. They prove that the volume form for the Randers metric \(F= a+\beta\) in a Randers space is just that for the Riemannian metric \(a\) and, as a consequence, the Bernstein type theorem in the special Randers space of dimension \(\leq 8\) is true. Also they prove a Bernstein type theorem in the 3-dimensional Minkowski space.

MSC:

53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)
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