Infinitesimal automorphisms and deformations of parabolic geometries

Čap, Andreas. "Infinitesimal automorphisms and deformations of parabolic geometries." Journal of the European Mathematical Society 010.2 (2008): 415-437. <http://eudml.org/doc/277723>.

@article{Čap2008,
abstract = {We show that infinitesimal automorphisms and infinitesimal deformations of parabolic geometries can be nicely described in terms of the twisted de Rham sequence associated to a certain linear connection on the adjoint tractor bundle. For regular normal geometries, this description can be related to the underlying geometric structure using the machinery of BGG sequences. In the locally flat case, this leads to a deformation complex, which generalizes the well known complex for locally conformally flat manifolds. Recently, a theory of subcomplexes in BGG sequences has been developed. This applies to certain types of torsion free parabolic geometries including quaternionic structures, quaternionic contact structures and CR structures. We show that for these structures one of the subcomplexes in the adjoint BGG sequence leads (even in the curved case) to a complex governing deformations in the subcategory of torsion free geometries. For quaternionic structures, this deformation complex is elliptic.},
author = {Čap, Andreas},
journal = {Journal of the European Mathematical Society},
keywords = {parabolic geometry; BGG--sequence; quaternionic structure; quaternionic contact structure; CR structure; infinitesimal automorphism; infinitesimal deformation; deformation complex; parabolic geometry; BGG sequence; quaternionic structure; quaternionic contact structure; CR structure; infinitesimal automorphism; infinitesimal deformation; deformation complex},
language = {eng},
number = {2},
pages = {415-437},
publisher = {European Mathematical Society Publishing House},
title = {Infinitesimal automorphisms and deformations of parabolic geometries},
url = {http://eudml.org/doc/277723},
volume = {010},
year = {2008},
}

TY - JOUR
AU - Čap, Andreas
TI - Infinitesimal automorphisms and deformations of parabolic geometries
JO - Journal of the European Mathematical Society
PY - 2008
PB - European Mathematical Society Publishing House
VL - 010
IS - 2
SP - 415
EP - 437
AB - We show that infinitesimal automorphisms and infinitesimal deformations of parabolic geometries can be nicely described in terms of the twisted de Rham sequence associated to a certain linear connection on the adjoint tractor bundle. For regular normal geometries, this description can be related to the underlying geometric structure using the machinery of BGG sequences. In the locally flat case, this leads to a deformation complex, which generalizes the well known complex for locally conformally flat manifolds. Recently, a theory of subcomplexes in BGG sequences has been developed. This applies to certain types of torsion free parabolic geometries including quaternionic structures, quaternionic contact structures and CR structures. We show that for these structures one of the subcomplexes in the adjoint BGG sequence leads (even in the curved case) to a complex governing deformations in the subcategory of torsion free geometries. For quaternionic structures, this deformation complex is elliptic.
LA - eng
KW - parabolic geometry; BGG--sequence; quaternionic structure; quaternionic contact structure; CR structure; infinitesimal automorphism; infinitesimal deformation; deformation complex; parabolic geometry; BGG sequence; quaternionic structure; quaternionic contact structure; CR structure; infinitesimal automorphism; infinitesimal deformation; deformation complex
UR - http://eudml.org/doc/277723
ER -