Universität zu Köln

Evers, Christian (2017). Real contact geometry. PhD thesis, Universität zu Köln.

Preview

PDF evers.pdf Download (773kB)

Abstract

The present thesis is devoted to the study of real contact manifolds. These are contact manifolds that carry an additional involution $f$, of which one requires the anti-symmetry condition $f_\ast\xi=-\xi$. Amongst others, real contact manifolds appear in Hamilton's description of mechanical systems as hyperplanes in phase spaces, for example in the three body problem. This text offers an introduction both to the theories of contact manifolds and involutions. In the first chapter, fundamental properties are studied on the basis of various examples. We observe that real contact manifolds establish a connection between two outstanding problems in contact geometry, specifically the Weinstein conjecture and Arnold's chord conjecture. The second chapter contains a collection of structure theorems for real contact manifolds, including Gray stability, Darboux's theorem, neighbourhood theorems for submanifolds, and a classification result for real structures compatible with the standard contact form in euclidean space. In the third chapter, we investigate two methods for constructing real contact manifolds, namely real open books and real surgery. The latter are introduced in the framework of real symplectic cobordisms.

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Evers, Christian cevers@math.uni-koeln.de UNSPECIFIED UNSPECIFIED
Corporate Creators:	Universität zu Köln
URN:	urn:nbn:de:hbz:38-77941
Date:	2017
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	Mathematics
Uncontrolled Keywords:	Keywords Language Contact geometry, involutions, real contact manifolds English
Date of oral exam:	28 June 2017
Referee:	Name Academic Title Geiges, Hansjörg Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/7794