Generalized complex submanifolds

Research output: Contribution to journalArticle

5 Citations (Scopus)

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
StatePublished - May 1 2008

Fingerprint

Submanifolds
Spinors
Poisson Structure
Complex Manifolds
Complex Structure
Involution
Paul Adrien Maurice Dirac
Locus
Siméon Denis Poisson

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

@article{db19086b72b84c9382c1dd64b0c72c38,
title = "Generalized complex submanifolds",
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 K{\"a}hler submanifolds.",
author = "James Barton and Stienon, {Mathieu Philippe}",
year = "2008",
month = "5",
day = "1",
doi = "10.2140/pjm.2008.236.23",
language = "English (US)",
volume = "236",
pages = "23--44",
journal = "Pacific Journal of Mathematics",
issn = "0030-8730",
publisher = "University of California, Berkeley",
number = "1",

}

Generalized complex submanifolds. / Barton, James; Stienon, Mathieu Philippe.

In: Pacific Journal of Mathematics, Vol. 236, No. 1, 01.05.2008, p. 23-44.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Generalized complex submanifolds

AU - Barton, James

AU - Stienon, Mathieu Philippe

PY - 2008/5/1

Y1 - 2008/5/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=62749124359&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=62749124359&partnerID=8YFLogxK

U2 - 10.2140/pjm.2008.236.23

DO - 10.2140/pjm.2008.236.23

M3 - Article

AN - SCOPUS:62749124359

VL - 236

SP - 23

EP - 44

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 1

ER -