Geodesic
Infinitesimal automorphisms and deformations of parabolic geometries
Journal of the European Mathematical Society, Tome 10 (2008) no. 2, pp. 415-437

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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.
DOI : 10.4171/jems/116
Classification : 53-XX, 58-XX, 00-XX
Keywords: Parabolic geometry, BGG--sequence, quaternionic structure, quaternionic contact structure, CR structure, infinitesimal automorphism, infinitesimal deformation, deformation complex 
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     author = {Andreas Cap},
     title = {Infinitesimal automorphisms and deformations of parabolic geometries},
     journal = {Journal of the European Mathematical Society},
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Andreas Cap. Infinitesimal automorphisms and deformations of parabolic geometries. Journal of the European Mathematical Society, Tome 10 (2008) no. 2, pp. 415-437. doi: 10.4171/jems/116

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