Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Complex Paraconformal Manifolds – their Differential Geometry and Twistor Theory

Complex Paraconformal Manifolds – their Differential Geometry and Twistor Theory Abstract. A complex paraconformal manifold is a/^-dimensional complex manifold (/?, q > 2) whose tangent bündle factors äs a tensor product of two bundles of ranks p and q. We also assume that we are given a fixed isomorphism of the highest exterior powers of the two bundles. Examples of such manifolds include 4-dimensional conformal manifolds (with spin structure) and complexified quaternionic, quaternionic Kahler and hyperKähler manifolds. We develop the differential geomety of these structures, which is formally very similar to that of the special case of four dimensional conformal structures [30]. The examples have the property that they have a rieh twistor theory, which we discuss in a unified way in the paraconformal category. In particular, we consider the 'non-linear graviton' construction [29], and discuss the structure on the twistor space corresponding to quaternionic Kahler and hyperKähler metrics. We also define a family of special curves for these structures which in the 4-dimensional conformal case coincide with the conformal circles [34,2]. These curves have an intrinsic, naturally defined projective structure. In the particular case of complexified 4Ä>dimensional quaternionic structures, we obtain a distinguished 8fc + l parameter family of special curves saüsfying a third order ODE in http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

Complex Paraconformal Manifolds – their Differential Geometry and Twistor Theory

Forum Mathematicum , Volume 3 (3) – Jan 1, 1991

Loading next page...
 
/lp/de-gruyter/complex-paraconformal-manifolds-their-differential-geometry-and-PtAQXQYcCA

References (28)

Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/form.1991.3.61
Publisher site
See Article on Publisher Site

Abstract

Abstract. A complex paraconformal manifold is a/^-dimensional complex manifold (/?, q > 2) whose tangent bündle factors äs a tensor product of two bundles of ranks p and q. We also assume that we are given a fixed isomorphism of the highest exterior powers of the two bundles. Examples of such manifolds include 4-dimensional conformal manifolds (with spin structure) and complexified quaternionic, quaternionic Kahler and hyperKähler manifolds. We develop the differential geomety of these structures, which is formally very similar to that of the special case of four dimensional conformal structures [30]. The examples have the property that they have a rieh twistor theory, which we discuss in a unified way in the paraconformal category. In particular, we consider the 'non-linear graviton' construction [29], and discuss the structure on the twistor space corresponding to quaternionic Kahler and hyperKähler metrics. We also define a family of special curves for these structures which in the 4-dimensional conformal case coincide with the conformal circles [34,2]. These curves have an intrinsic, naturally defined projective structure. In the particular case of complexified 4Ä>dimensional quaternionic structures, we obtain a distinguished 8fc + l parameter family of special curves saüsfying a third order ODE in

Journal

Forum Mathematicumde Gruyter

Published: Jan 1, 1991

There are no references for this article.