Results 1 to 10 of about 150 (110)
k-Dirac Operator and Parabolic Geometries [PDF]
Complex Analysis and Operator Theory, 2013 The principal group of a Klein geometry has canonical left action on the homogeneous space of the geometry and this action induces action on the spaces of sections of vector bundles over the homogeneous space. This paper is about construction of differential operators invariant with respect to the induced action of the principal group of a particular ...
Tomáš Salac
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On Distinguished Curves in Parabolic Geometries
Transformation Groups, 2004 All parabolic geometries, i.e. Cartan geometries with homogeneous model a real generalized flag manifold, admit highly interesting classes of distinguished curves. The geodesics of a projective class of connections on a manifold, conformal circles on conformal Riemannian manifolds, and Chern--Moser chains on CR--manifolds of hypersurface type are ...
Andreas Cap +2 more
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Symmetries of parabolic geometries
Differential Geometry and Its Applications, 2009 We generalize the concept of affine locally symmetric spaces for parabolic geometries. We discuss mainly $|1|$--graded geometries and we show some restrictions on their curvature coming from the existence of symmetries. We use the theory of Weyl structures to discuss more interesting $|1|$--graded geometries which can carry a symmetry in a point with ...
Lenka Zalabová
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Cone structures and parabolic geometries [PDF]
Mathematische Annalen, 2021 39 ...
Jun-Muk Hwang +2 more
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Holomorphic Parabolic Geometries and Calabi-Yau Manifolds [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2011 We prove that the only complex parabolic geometries on Calabi-Yau manifolds are the homogeneous geometries on complex tori. We also classify the complex parabolic geometries on homogeneous compact Kähler manifolds.
Benjamin McKay
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Minimal Parabolic Geometries for the Sporadic Groups
European Journal of Combinatorics, 1984 Most of the finite simple groups are of Lie type, and these act on geometries called Tits buildings [\textit{J. Tits}, Buildings of spherical type, Lect. Notes Math. 386 (1974; Zbl 0295.20047)]. Analogous geometries for sporadic simple groups were first studied by \textit{F. Buekenhout} [J. Comb. Theory, Ser.
G Stroth
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Critical behaviour in parabolic geometries [PDF]
Journal of Physics A, 1991 We study two-dimensional systems with boundary curves described by power laws. Using conformal mappings we obtain the correlations at the bulk critical point. Three different classes of behaviour are found and explained by scaling arguments which also apply to higher dimensions.
I Peschel, L Turban, F Igloi
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Subriemannian Metrics and the Metrizability of Parabolic Geometries [PDF]
Journal of Geometric Analysis, 2019 25 ...
David M J Calderbank +2 more
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Complete complex parabolic geometries [PDF]
International Mathematics Research Notices, 2006 Complete complex parabolic geometries (including projective connections and conformal connections) are flat and homogeneous. This is the first global theorem on parabolic geometries.
Benjamin Mckay, Mckay Benjamin
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Non-rigid parabolic geometries of Monge type
Advances in Mathematics, 2015 In this paper we study a novel class of parabolic geometries which we call parabolic geometries of Monge type. These parabolic geometries are defined by special gradings of simple Lie algebras, namely, gradings with the property that their -1 component contains a nonzero co-dimension 1 abelian subspace whose bracket with its complement is non ...
Zhaohu Nie, Paweł Nurowski
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