The Srní lectures on non-integrable geometries with torsion
Archivum Mathematicum (2006)
- Volume: 042, Issue: 5, page 5-84
- ISSN: 0044-8753
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topAgricola, Ilka. "The Srní lectures on non-integrable geometries with torsion." Archivum Mathematicum 042.5 (2006): 5-84. <http://eudml.org/doc/18858>.
@article{Agricola2006,
abstract = {This review article intends to introduce the reader to non-integrable geometric structures on Riemannian manifolds and invariant metric connections with torsion, and to discuss recent aspects of mathematical physics—in particular superstring theory—where these naturally appear. Connections with skew-symmetric torsion are exhibited as one of the main tools to understand non-integrable geometries. To this aim a a series of key examples is presented and successively dealt with using the notions of intrinsic torsion and characteristic connection of a $G$-structure as unifying principles. The General Holonomy Principle bridges over to parallel objects, thus motivating the discussion of geometric stabilizers, with emphasis on spinors and differential forms. Several Weitzenböck formulas for Dirac operators associated with torsion connections enable us to discuss spinorial field equations, such as those governing the common sector of type II superstring theory. They also provide the link to Kostant’s cubic Dirac operator.},
author = {Agricola, Ilka},
journal = {Archivum Mathematicum},
keywords = {metric connection with torsion; intrinsic torsion; $G$-structure; characteristic connection; superstring theory; Strominger model; parallel spinor; non-integrable geometry; integrable geometry; Berger’s holonomy theorem; naturally reductive space; hyper-Kähler manifold with torsion; almost metric contact structure; $G_2$-manifold; $(7)$-manifold; $(3)$-structure; $3$-Sasakian manifold; metric connection with torsion; intrinsic torsion; -structure; characteristic connection; superstring theory},
language = {eng},
number = {5},
pages = {5-84},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {The Srní lectures on non-integrable geometries with torsion},
url = {http://eudml.org/doc/18858},
volume = {042},
year = {2006},
}
TY - JOUR
AU - Agricola, Ilka
TI - The Srní lectures on non-integrable geometries with torsion
JO - Archivum Mathematicum
PY - 2006
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 5
SP - 5
EP - 84
AB - This review article intends to introduce the reader to non-integrable geometric structures on Riemannian manifolds and invariant metric connections with torsion, and to discuss recent aspects of mathematical physics—in particular superstring theory—where these naturally appear. Connections with skew-symmetric torsion are exhibited as one of the main tools to understand non-integrable geometries. To this aim a a series of key examples is presented and successively dealt with using the notions of intrinsic torsion and characteristic connection of a $G$-structure as unifying principles. The General Holonomy Principle bridges over to parallel objects, thus motivating the discussion of geometric stabilizers, with emphasis on spinors and differential forms. Several Weitzenböck formulas for Dirac operators associated with torsion connections enable us to discuss spinorial field equations, such as those governing the common sector of type II superstring theory. They also provide the link to Kostant’s cubic Dirac operator.
LA - eng
KW - metric connection with torsion; intrinsic torsion; $G$-structure; characteristic connection; superstring theory; Strominger model; parallel spinor; non-integrable geometry; integrable geometry; Berger’s holonomy theorem; naturally reductive space; hyper-Kähler manifold with torsion; almost metric contact structure; $G_2$-manifold; $(7)$-manifold; $(3)$-structure; $3$-Sasakian manifold; metric connection with torsion; intrinsic torsion; -structure; characteristic connection; superstring theory
UR - http://eudml.org/doc/18858
ER -
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