Some special geometry in dimension six

Čap, Andreas; Eastwood, Michael

  • Proceedings of the 22nd Winter School "Geometry and Physics", Publisher: Circolo Matematico di Palermo(Palermo), page [93]-98

Abstract

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Motivated by the study of CR-submanifolds of codimension  2 in  ℂ 4 , the authors consider here a 6 -dimensional oriented manifold  M equipped with a 4 -dimensional distribution. Under some non-degeneracy condition, two different geometric situations can occur. In the elliptic case, one constructs a canonical almost complex structure on  M ; the hyperbolic case leads to a canonical almost product structure. In both cases the only local invariants are given by the obstructions to integrability for these structures. The local ’flat’ models are a 3 -dimensional complex contact manifold and the product of two 3 -dimensional real contact manifolds, respectively.

How to cite

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Čap, Andreas, and Eastwood, Michael. "Some special geometry in dimension six." Proceedings of the 22nd Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 2003. [93]-98. <http://eudml.org/doc/220231>.

@inProceedings{Čap2003,
abstract = {Motivated by the study of CR-submanifolds of codimension $2$ in $\mathbb \{C\}^4$, the authors consider here a $6$-dimensional oriented manifold $M$ equipped with a $4$-dimensional distribution. Under some non-degeneracy condition, two different geometric situations can occur. In the elliptic case, one constructs a canonical almost complex structure on $M$; the hyperbolic case leads to a canonical almost product structure. In both cases the only local invariants are given by the obstructions to integrability for these structures. The local ’flat’ models are a $3$-dimensional complex contact manifold and the product of two $3$-dimensional real contact manifolds, respectively.},
author = {Čap, Andreas, Eastwood, Michael},
booktitle = {Proceedings of the 22nd Winter School "Geometry and Physics"},
keywords = {Winter school; Geometry; Physics; Srní (Czech Republic)},
location = {Palermo},
pages = {[93]-98},
publisher = {Circolo Matematico di Palermo},
title = {Some special geometry in dimension six},
url = {http://eudml.org/doc/220231},
year = {2003},
}

TY - CLSWK
AU - Čap, Andreas
AU - Eastwood, Michael
TI - Some special geometry in dimension six
T2 - Proceedings of the 22nd Winter School "Geometry and Physics"
PY - 2003
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [93]
EP - 98
AB - Motivated by the study of CR-submanifolds of codimension $2$ in $\mathbb {C}^4$, the authors consider here a $6$-dimensional oriented manifold $M$ equipped with a $4$-dimensional distribution. Under some non-degeneracy condition, two different geometric situations can occur. In the elliptic case, one constructs a canonical almost complex structure on $M$; the hyperbolic case leads to a canonical almost product structure. In both cases the only local invariants are given by the obstructions to integrability for these structures. The local ’flat’ models are a $3$-dimensional complex contact manifold and the product of two $3$-dimensional real contact manifolds, respectively.
KW - Winter school; Geometry; Physics; Srní (Czech Republic)
UR - http://eudml.org/doc/220231
ER -

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