Asian Journal of Mathematics

Volume 10 (2006)

Number 3

Brackets, forms and invariant functionals

Pages: 541 – 560

DOI: http://dx.doi.org/10.4310/AJM.2006.v10.n3.a3

Author

Nigel Hitchin

Abstract

In the context of generalized geometry we first show how the Courant bracket helps to define connections with skew torsion and then investigate a five-dimensional invariant functional and its associated geometry, which involves three Courant-commuting sections of $T \bigoplus T\sp *$ . A Hamiltonian flow arising from this corresponds to a version of the Nahm equations, and we investigate the sixdimensional geometrical structure this describes.

Keywords

Generalized geometry; Courant bracket; skew torsion; gerbe

2010 Mathematics Subject Classification

53C25, 53C80

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