3 citations · 14 across the 12 of their papers we have counts for
14 papers
Strong Ramadanov Conjecture for Real Ellipsoids in : two approaches
Jan Gregorovic, Ilya Kossovskiy, Son-Ying Li +1
In this paper, we provide two (significantly different) proofs of the well known Strong Ramadanov Conjecture for the class of real ellipsoids in the complex -space.
Irreducible Killing and conformal Killing tensors on homogeneous plane waves
Jan Gregorovič, Lenka Zalabová
This paper presents a classification of irreducible Killing and conformal Killing 2-tensors on homogeneous plane waves, a specific class of Lorentzian metrics on four-dimensional m…
Curvature of quaternionic skew-Hermitian manifolds and bundle constructions
Ioannis Chrysikos, Vicente Cortés, Jan Gregorovič
This articles is devoted to a description of the second-order differential geometry of torsion-free almost quaternionic skew-Hermitian manifolds, that is, of quaternionic skew-Herm…
The jet transcendence degree of a real hypersurface and Huang-Ji-Yau Conjecture
Jan Gregorovic, Ilya Kossovskiy
We investigate the problem of holomorphic algebraizibility for real hypersurfaces in complex space. We introduce a new invariant of a (real-analytic) Levi-nondegenerate hypersurfac…
The gap phenomenon for conformally related Einstein metrics
Jan Gregorovič, Josef Šilhan
We determine the submaximal dimensions of the spaces of almost Einstein scales and normal conformal Killing fields for connected conformal manifolds. The results depend on the sign…
First BGG operators on homogeneous conformal geometries
Jan Gregorovič, Lenka Zalabová
We study first BGG operators and their solutions on homogeneous conformal geometries. We focus on conformal Killing tensors, conformal Killing--Yano forms and twistor spinors in pa…
Differential geometry of -type structures -- Integrability
Ioannis Chrysikos, Jan Gregorovič, Henrik Winther
We study almost hypercomplex skew-Hermitian structures and almost quaternionic skew-Hermitian structures, as the geometric structures underlying - and $\maths…
Differential geometry of -type structures
Ioannis Chrysikos, Jan Gregorovič, Henrik Winther
We study -dimensional smooth manifolds admitting a - or a -structure, where is the quaternionic real for…
First BGG operators via homogeneous examples
Jan Gregorovič, Lenka Zalabová
We review the theory of first BGG operators and study how to approach them and find their solution on homogeneous geometries. We provide many new examples of parabolic geometries t…
On the Beloshapka's rigidity conjecture for real submanifolds in complex space
Jan Gregorovic
A well known Conjecture due to Beloshapka asserts that all totally nondegenerate polynomial models with the length of their Levi-Tanaka algebra are {\em rigid}, that is,…
On symmetric CR geometries of hypersurface type
Jan Gregorovič, Lenka Zalabová
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 p…
Geometric properties of homogeneous parabolic geometries with generalized symmetries
Jan Gregorovič, Lenka Zalabová
We investigate geometric properties of homogeneous parabolic geometries with generalized symmetries. We show that they can be reduced to a simpler geometric structures and interpre…
On automorphisms with natural tangent actions on homogeneous parabolic geometries
Jan Gregorovič, Lenka Zalabová
We consider automorphisms of homogeneous parabolic geometries with a fixed point. Parabolic geometries carry the distinguished distributions and we study those automorphisms which…
Classification of invariant AHS--structures on semisimple locally symmetric spaces
Jan Gregorovič
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 d…