On local flatness of manifolds with AHS-structures

Čap, Andreas; Slovák, Jan

  • Proceedings of the 15th Winter School "Geometry and Physics", Publisher: Circolo Matematico di Palermo(Palermo), page [95]-101

Abstract

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Summary: The AHS-structures on manifolds are the simplest cases of the so called parabolic geometries which are modeled on homogeneous spaces corresponding to a parabolic subgroup in a semisimple Lie group. It covers the cases where the negative parts of the graded Lie algebras in question are abelian. In the series the authors developed a consistent frame bundle approach to the subject. Here we give explicit descriptions of the obstructions against the flatness of such structures based on the latter approach. In particular we recover the results proved by Baston for complex manifolds in the real smooth setting.

How to cite

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Čap, Andreas, and Slovák, Jan. "On local flatness of manifolds with AHS-structures." Proceedings of the 15th Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 1996. [95]-101. <http://eudml.org/doc/220669>.

@inProceedings{Čap1996,
abstract = {Summary: The AHS-structures on manifolds are the simplest cases of the so called parabolic geometries which are modeled on homogeneous spaces corresponding to a parabolic subgroup in a semisimple Lie group. It covers the cases where the negative parts of the graded Lie algebras in question are abelian. In the series the authors developed a consistent frame bundle approach to the subject. Here we give explicit descriptions of the obstructions against the flatness of such structures based on the latter approach. In particular we recover the results proved by Baston for complex manifolds in the real smooth setting.},
author = {Čap, Andreas, Slovák, Jan},
booktitle = {Proceedings of the 15th Winter School "Geometry and Physics"},
keywords = {Proceedings; Geometry; Physics; Winter school; Srni (Czech Republic)},
location = {Palermo},
pages = {[95]-101},
publisher = {Circolo Matematico di Palermo},
title = {On local flatness of manifolds with AHS-structures},
url = {http://eudml.org/doc/220669},
year = {1996},
}

TY - CLSWK
AU - Čap, Andreas
AU - Slovák, Jan
TI - On local flatness of manifolds with AHS-structures
T2 - Proceedings of the 15th Winter School "Geometry and Physics"
PY - 1996
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [95]
EP - 101
AB - Summary: The AHS-structures on manifolds are the simplest cases of the so called parabolic geometries which are modeled on homogeneous spaces corresponding to a parabolic subgroup in a semisimple Lie group. It covers the cases where the negative parts of the graded Lie algebras in question are abelian. In the series the authors developed a consistent frame bundle approach to the subject. Here we give explicit descriptions of the obstructions against the flatness of such structures based on the latter approach. In particular we recover the results proved by Baston for complex manifolds in the real smooth setting.
KW - Proceedings; Geometry; Physics; Winter school; Srni (Czech Republic)
UR - http://eudml.org/doc/220669
ER -

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