Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 24, No. 1, pp. 155-168 (2008)

On the geometry of two-step nilpotent groups with left invariant Finsler metrics

A. Tóth and Z. Kovács

University of Debrecen, College of Nyíregyháza

Abstract: We begin a systematic study of these spaces following Eberlein's comprehensive study in the Riemannian case. In particular, for some special groups (including Heisenberg groups) we give an explicit form for the Chern-Rund connection, study the curvature and the flag curvature, and derive the equations of relative geodesics.

Keywords: 2-step nilpotent Lie algebra, left-invariant Finsler metric, curvature of Finsler spaces

Classification (MSC2000): 53B40

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