Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 5 (2009), 086, 15 pages      arXiv:0909.0478
Contribution to the Special Issue “Élie Cartan and Differential Geometry”

Natural Intrinsic Geometrical Symmetries

Stefan Haesen a and Leopold Verstraelen b
a) Simon Stevin Institute for Geometry, Wilhelminaweg 1, 2042 NN Zandvoort, The Netherlands
b) Katholieke Universiteit Leuven, Department of Mathematics, Celestijnenlaan 200B bus 2400, B-3000 Leuven, Belgium

Received April 08, 2009, in final form August 25, 2009; Published online September 02, 2009; Theorem 20 is corrected and References [13, 14] are added October 06, 2009

A proposal is made for what could well be the most natural symmetrical Riemannian spaces which are homogeneous but not isotropic, i.e. of what could well be the most natural class of symmetrical spaces beyond the spaces of constant Riemannian curvature, that is, beyond the spaces which are homogeneous and isotropic, or, still, the spaces which satisfy the axiom of free mobility.

Key words: parallel transport; holonomy; spaces of constant curvature; pseudo-symmetry.

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