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Generalized Complex Submanifolds

Research paper by James Barton, Mathieu Stienon

Indexed on: 07 Apr '07Published on: 07 Apr '07Published in: Mathematics - Differential Geometry



Abstract

We introduce the notion of twisted generalized complex submanifolds and describe an equivalent characterization in terms of Poisson-Dirac submanifolds. Our characterization recovers a result of Vaisman. An equivalent characterization is also given in terms of spinors. As a consequence, we show that the fixed locus of an involution preserving a twisted generalized complex structure is a twisted generalized complex submanifold. We also prove that a twisted generalized complex manifold has a natural Poisson structure. We also discuss generalized Kaehler submanifolds.