3,148 research outputs found
Adapted connections on metric contact manifolds
In this paper, we describe the space of adapted connections on a metric
contact manifold through the space of their torsion tensors. The torsion tensor
is an element of the space of TM-valued two-forms, which splits into various
subspaces. We study the parts of the torsion tensor according to this splitting
to completely describe the space of adapted connections. We use this
description to obtain characterizations of the generalized Tanaka-Webster
connection and to describe the Dirac operators of adapted connections.Comment: 25 pages; some remarks added, minor correction
A Berger-type theorem for metric connections with skew-symmetric torsion
We prove a Berger-type theorem which asserts that if the orthogonal subgroup
generated by the torsion tensor (pulled back to a point by parallel transport)
of a metric connection with skew-symmetric torsion is not transitive on the
sphere, then the space must be locally isometric to a Lie group with a
bi-invariant metric or its symmetric dual (we assume the space to be locally
irreducible). We also prove that a (simple) Lie group with a bi-invariant
metric admits only two flat metric connections with skew-symmetric torsion: the
two flat canonical connections. In particular, we get a refinement of a
well-known theorem by Cartan and Schouten. Finally, we show that the holonomy
group of a metric connection with skew-symmetric torsion on these spaces
generically coincides with the Riemannian holonomy.Comment: 13 pages; we add some new examples and fix minor misprints; final
version to appear in Journal of Geometry and Physic
The Gaussian Measure On Algebraic Varieties
We prove that the ring \Aff{\R}{M} of all polynomials defined on a real
algebraic variety is dense in the Hilbert space
L^2(M,e^{-|x|^2}\de\mu), where \de\mu denotes the volume form of and
\de\nu=e^{-|x|^2}\de\mu the Gaussian measure on .Comment: Latex2.09, 6 page
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