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Finsler Spaces and Their Generalizations

  • V. I. Bliznikas
Part of the Progress in Mathematics book series (PM, volume 9)

Abstract

Right up to today the ideas of Riemann determine the path of progress in the differential geometry of generalized spaces. These ideas are based on the possibility of the geometrization of the theory of differential invariants relative to some transformation group. This geometrization leans on analogy to the extent that the types of invariants being studied are encountered in the differential geometry of Euclidean space (or of some other Klein space). The generalization consists in the rejection of some relations or others which are characteristic of Klein geometry (in particular, of Euclidean geometry). The first generalization of Riemann geometry (the theory of the invariants of a quadratic differential forfn) is due to Finsler [203, 204] who considered that the square of the arc length element of a curve is an arbitrary homogeneous function of the differentials of the local coordinates of the point. * Certain aspects of Finsler geometry were considered also by Noether [406, 407].

Keywords

Line Element Curvature Tensor Constant Scalar Curvature Finsler Space Minimal Hypersurface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Plenum Press, New York 1971

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  • V. I. Bliznikas

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