Constant curvature models in sub-Riemannian geometry

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Authors

ALEKSEEVSKIY Dmitry MEDVEDEV Alexandr SLOVÁK Jan

Year of publication 2019
Type Article in Periodical
Magazine / Source Journal of Geometry and Physics
MU Faculty or unit

Faculty of Science

Citation
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Doi http://dx.doi.org/10.1016/j.geomphys.2018.09.013
Keywords Curvature; SubRiemannian geometry; Lie algebra cohomology; Constant curvature spaces
Description Each sub-Riemannian geometry with bracket generating distribution enjoys a background structure determined by the distribution itself. At the same time, those geometries with constant sub-Riemannian symbols determine a unique Cartan connection leading to their principal invariants. We provide cohomological description of the structure of these curvature invariants in the cases where the background structure is one of the parabolic geometries. As an illustration, constant curvature models are discussed for certain sub-Riemannian geometries.
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