Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 24, No. 1, pp. 25-31 (2008)

On the rectilinear extremals of geodesics in Sol geometry

S. Bácsó and B. Szilágyi

Debrecen University, Budapest University of Technology and Economics

Abstract: In this paper we deal with one of the homogeneous geometries, the Sol geometry. The goal of this publication is to show that there does not exist rectilinear extremals of geodesics. During the proof we consider the Riemannian space with Sol metric as a special Finsler space and applied Finslerian methods.

Keywords: Homogeneous Riemannian geometry, geodesic, Finsler metric

Classification (MSC2000): 53B20

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