Analog of selfduality in dimension nine
Anna Fino,Pawel Nurowski +1 more
Reads0
Chats0
TLDR
In this paper, the authors introduce a type of Riemannian geometry in nine dimen- sions, which can be viewed as the counterpart of selfduality in four dimen sions.Abstract:
We introduce a type of Riemannian geometry in nine dimen- sions, which can be viewed as the counterpart of selfduality in four dimen- sions. This geometry is related to a 9-dimensional irreducible representation of SO(3) SO(3) and it turns out to be defined by a dierential 4-form. Structures admitting a metric connection with totally antisymmetric torsion and preserving the 4-form are studied in detail, producing locally homogeneous examples which can be viewed as analogs of self-dual 4-manifolds in dimension nine.read more
Citations
More filters
Posted Content
On the topology and the geometry of SO(3)-manifolds
TL;DR: In this article, the authors studied the topology and the differential geometry of 5-dimensional Riemannian manifolds with SO(3) irreducible structure, i.e., with a reduction of the frame bundle to SO( 3) ǫ-ir.
Posted Content
Extensions of the coeffective complex
TL;DR: The coeffective differential complex on a symplectic manifold was extended in this article, which unifies the constructions of various other authors, including the authors of this paper. But the extension was not extended in this work.
References
More filters
Journal ArticleDOI
Self-duality in four-dimensional Riemannian geometry
TL;DR: In this article, the authors present a self-contained account of the ideas of R. Penrose connecting four-dimensional Riemannian geometry with three-dimensional complex analysis, and apply this to the self-dual Yang-Mills equations in Euclidean 4-space and compute the number of moduli for any compact gauge group.
Book
Classical invariant theory
TL;DR: There has been a resurgence of interest in classical invariant theory driven by several factors: new theoretical developments; a revival of computational methods coupled with powerful new computer algebra packages; and a wealth of new applications, ranging from number theory to geometry, physics to computer vision as mentioned in this paper.
Journal ArticleDOI
On the holonomy of connections with skew-symmetric torsion
Ilka Agricola,Thomas Friedrich +1 more
TL;DR: In this paper, the authors investigated the holonomy group of a linear metric connection with skew-symmetric torsion and showed that it is always semisimple and does not preserve any non-degenerated 2-form or any spinor.
Posted Content
The Srni lectures on non-integrable geometries with torsion
TL;DR: In this article, the authors introduce the reader to non-integrable geometric structures on Riemannian manifolds and invariant metric connections with torsion, and discuss recent aspects of mathematical physics where these naturally appear.
Posted Content
Prolongations of Lie algebras and applications
TL;DR: In this paper, the authors studied the skew-symmetric prolongation of a Lie subalgebra and derived the holonomy representation of metric connections with vectorial torsion.