Construction of counterexamples to the 2–jet determination Chern–Moser Theorem in higher codimension

Autor: Jan Gregorovič, Francine Meylan

Publikováno v: Mathematical Research Letters. 29:399-420

We first construct a counterexample of a generic quadratic submanifold of codimension $5$ in $\Bbb C^9$ which admits a real analytic infinitesimal CR automorphism with homogeneous polynomial coefficients of degree $4.$ This example also resolves a qu

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https://doi.org/10.4310/mrl.2022.v29.n2.a4

On Symmetric CR Geometries of Hypersurface Type

Autor: Lenka Zalabová, Jan Gregorovič

Publikováno v: The Journal of Geometric Analysis. 29:3135-3159

We study non-degenerate CR geometries of hypersurface type that are symmetric in the sense that, at each point, there is a CR transformation reversing the CR distribution at that point. We show that such geometries are either flat or homogeneous. We

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https://doi.org/10.1007/s12220-018-00110-1

A construction of non-flat non-homogeneous symmetric parabolic geometries

Autor: Jan Gregorovič, Lenka Zalabová

Publikováno v: Archivum Mathematicum. :291-302

We construct a series of examples of non--flat non--homogeneous parabolic geometries that carry a symmetry of the parabolic geometry at each point.
12 pp, submitted to Archivum Mathematicum

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https://doi.org/10.5817/am2016-5-291

Classification of invariant AHS-structures on semisimple locally symmetric spaces

Autor: Jan Gregorovič

Publikováno v: Open Mathematics, Vol 11, Iss 12, Pp 2062-2075 (2013)
Gregorovic, J 2013, ' Classification of invariant AHS-structures on semisimple locally symmetric spaces ', Central European Journal of Mathematics, vol. 11, no. 12, pp. 2062-2075 . https://doi.org/10.2478/s11533-013-0318-5

In this article, we discuss which semisimple locally symmetric spaces admit an AHS--structure invariant to local symmetries. We classify them for all types of AHS--structures and determine possible equivalence classes of such AHS--structures.
su

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https://doaj.org/article/e042a5ef3f4c48eba6b6d2a1c7fee91f

Local Generalized Symmetries and Locally Symmetric Parabolic Geometries

Autor: Jan Gregorovič, Lenka Zalabová

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, w

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