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Finsler geometry; holonomy; infinite dimensional Lie algebra; Witt algebra
The aim of this paper is to determine explicitly the algebraic structure of the curvature algebra of the 3-dimensional Heisenberg group with left invariant cubic metric. We show, that this curvature algebra is an infinite dimensional graded Lie subalgebra of the generalized Witt algebra of homogeneous vector fields generated by three elements.
[1] Dokovic, D.Z., Zhao, K.: Derivations, isomorphisms, and second cohomology of generalized Witt algebras. T. Am. Math. Soc., 350, 2, 1998, 643-664 DOI 10.1090/S0002-9947-98-01786-3 | MR 1390977
[2] Kawamoto, N.: Generalizations of Witt algebras over a field of characteristic zero. Hiroshima Math., 16, 1986, 417-426 MR 0855169 | Zbl 0607.17008
[3] Matsumoto, M.: Finsler Geometry in the 20th-Century, Handbook of Finsler Geometry. 2003, Kluwer Academic Publishers, 565--966. MR 2066451
[4] Muzsnay, Z., Nagy, P.T.: Finsler manifolds with non-Riemannian holonomy. Houston J. Math., 38, 2012, 77-92 MR 2917275 | Zbl 1238.53012
[5] Shen, Z.: Differential Geometry of Spray and Finsler Spaces. 2001, Kluwer Academic Publishers, Dordrecht MR 1967666 | Zbl 1009.53004
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