The Space of Integrable Dirac Structures on Hilbert C*-Modules

Details The Space of Integrable Dirac Structures on Hilbert C*-Modules The Space of Integrable Dirac Structures on Hilbert C*-Modules

2009-08-03

arxiv.org/abs/0908.0178v2

Mathematics

Differential Geometry

16 pages

Scientific paper

In this paper we interpret the integrability of the Dirac structures on some Hilbert C*-modules in terms of an automorphism group. This is the group of orthogonal transformations on the Hilbert C*-module of sections of a Hermitian vector bundle over an smooth manifold M. Some topological properties of the group of integrable Dirac structures are studied. In some special cases it is shown that the integrability condition corresponds to the solutions of a partial differential equation. This is explained as a necessary and sufficient condition.

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