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From Finsler geometry to noncommutative geometry. (English) Zbl 1093.53074

Summary: One link between Finsler geometry and noncommutative geometry is given by a differential operator, which is called the Dirac operator. In this paper, we construct such an operator and we analyze some of its properties. We also present an eloquent example. After, that we continue the construction of this operator for the case of Randers spaces, which are some particular example of Finsler spaces.

MSC:

53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
58B34 Noncommutative geometry (à la Connes)
53C27 Spin and Spin\({}^c\) geometry
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