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arXiv · 1607.01965

Local Generalized Symmetries and Locally Symmetric Parabolic Geometries

Jan Gregorovič·Lenka Zalabová
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Abstract

We investigate (local) automorphisms of parabolic geometries that generalize geodesic symmetries. We show that many types of parabolic geometries admit at most one generalized geodesic symmetry at a point with non-zero harmonic curvature. Moreover, we show that if there is exactly one symmetry at each point, then the parabolic geometry is a generalization of an affine (locally) symmetric space.

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Jan Gregorovič, Lenka Zalabová. 2016-07-07. Local Generalized Symmetries and Locally Symmetric Parabolic Geometries. https://doi.org/10.3842/sigma.2017.032

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