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Generalized Complex Submanifolds

James Barton·Mathieu Stienon
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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.

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James Barton, Mathieu Stienon. 2007-04-07. Generalized Complex Submanifolds. https://doi.org/10.2140/pjm.2008.236-1

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