Generalized complex submanifolds

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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 (2007). 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 Kähler submanifolds.

Original languageEnglish (US)
Pages (from-to)23-44
Number of pages22
JournalPacific Journal of Mathematics
Volume236
Issue number1
DOIs
Publication statusPublished - May 1 2008

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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