On types of non-integrable geometrie

Friedrich, Thomas. "On types of non-integrable geometrie." Proceedings of the 22nd Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 2003. [99]-113. <http://eudml.org/doc/220456>.

@inProceedings{Friedrich2003,
abstract = {A G-structure on a Riemannian manifold is said to be integrable if it is preserved by the Levi-Civita connection. In the presented paper, the following non-integrable G-structures are studied: SO(3)-structures in dimension 5; almost complex structures in dimension 6; G$_2$-structures in dimension 7; Spin(7)-structures in dimension 8; Spin(9)-structures in dimension 16 and F$_4$-structures in dimension 26. G-structures admitting an affine connection with totally skew-symmetric torsion are characterized. It is known [S. Ivanov, Connections with torsion, parallel spinors and geometry of Spin(7)-manifolds, math.dg/0111216] that any Spin(7)-structure admits a unique connection with totally skew-symmetric torsion. In this paper, it is proved that under weak conditions on the structure group this is the only geometric structure with that property. Moreover, the automorphisms group of non-integrable geometric structures are studied.},
author = {Friedrich, Thomas},
booktitle = {Proceedings of the 22nd Winter School "Geometry and Physics"},
keywords = {Winter school; Geometry; Physics; Srní (Czech Republic)},
location = {Palermo},
pages = {[99]-113},
publisher = {Circolo Matematico di Palermo},
title = {On types of non-integrable geometrie},
url = {http://eudml.org/doc/220456},
year = {2003},
}

TY - CLSWK
AU - Friedrich, Thomas
TI - On types of non-integrable geometrie
T2 - Proceedings of the 22nd Winter School "Geometry and Physics"
PY - 2003
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [99]
EP - 113
AB - A G-structure on a Riemannian manifold is said to be integrable if it is preserved by the Levi-Civita connection. In the presented paper, the following non-integrable G-structures are studied: SO(3)-structures in dimension 5; almost complex structures in dimension 6; G$_2$-structures in dimension 7; Spin(7)-structures in dimension 8; Spin(9)-structures in dimension 16 and F$_4$-structures in dimension 26. G-structures admitting an affine connection with totally skew-symmetric torsion are characterized. It is known [S. Ivanov, Connections with torsion, parallel spinors and geometry of Spin(7)-manifolds, math.dg/0111216] that any Spin(7)-structure admits a unique connection with totally skew-symmetric torsion. In this paper, it is proved that under weak conditions on the structure group this is the only geometric structure with that property. Moreover, the automorphisms group of non-integrable geometric structures are studied.
KW - Winter school; Geometry; Physics; Srní (Czech Republic)
UR - http://eudml.org/doc/220456
ER -