A Survey of Riemannian Contact Geometry

This survey is a presentation of the five lectures on Riemannian contact geometry that the author gave at the conference “RIEMain in Contact”, 18-22 June 2018 in Cagliari, Sardinia. The author was particularly pleased to be asked to give this presentation and appreciated the organizers’ kindness in...

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Autor principal:	Blair David E.
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2019
Materias:	Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/cae82b10ebb740ca8847db6055c43dd5
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id	oai:doaj.org-article:cae82b10ebb740ca8847db6055c43dd5
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spelling	oai:doaj.org-article:cae82b10ebb740ca8847db6055c43dd52021-12-02T19:08:48ZA Survey of Riemannian Contact Geometry2300-744310.1515/coma-2019-0002https://doaj.org/article/cae82b10ebb740ca8847db6055c43dd52019-01-01T00:00:00Zhttps://doi.org/10.1515/coma-2019-0002https://doaj.org/toc/2300-7443This survey is a presentation of the five lectures on Riemannian contact geometry that the author gave at the conference “RIEMain in Contact”, 18-22 June 2018 in Cagliari, Sardinia. The author was particularly pleased to be asked to give this presentation and appreciated the organizers’ kindness in dedicating the conference to him. Georges Reeb once made the comment that the mere existence of a contact form on a manifold should in some sense “tighten up” the manifold. The statement seemed quite pertinent for a conference that brought together both geometers and topologists working on contact manifolds, whether in terms of “tight” vs. “overtwisted” or whether an associated metric should have some positive curvature. The first section will lay down the basic definitions and examples of the subject of contact metric manifolds. The second section will be a continuation of the first discussing tangent sphere bundles, contact structures on 3-dimensional Lie groups and a brief treatment of submanifolds. Section III will be devoted to the curvature of contact metric manifolds. Section IV will discuss complex contact manifolds and some older style topology. Section V treats curvature functionals and Ricci solitons. A sixth section has been added giving a discussion of the question of whether a Riemannian metric g can be an associated metric for more than one contact structure; at the conference this was an addendum to the third lecture.Blair David E.De GruyterarticleMathematicsQA1-939ENComplex Manifolds, Vol 6, Iss 1, Pp 31-64 (2019)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mathematics QA1-939
spellingShingle	Mathematics QA1-939 Blair David E. A Survey of Riemannian Contact Geometry
description	This survey is a presentation of the five lectures on Riemannian contact geometry that the author gave at the conference “RIEMain in Contact”, 18-22 June 2018 in Cagliari, Sardinia. The author was particularly pleased to be asked to give this presentation and appreciated the organizers’ kindness in dedicating the conference to him. Georges Reeb once made the comment that the mere existence of a contact form on a manifold should in some sense “tighten up” the manifold. The statement seemed quite pertinent for a conference that brought together both geometers and topologists working on contact manifolds, whether in terms of “tight” vs. “overtwisted” or whether an associated metric should have some positive curvature. The first section will lay down the basic definitions and examples of the subject of contact metric manifolds. The second section will be a continuation of the first discussing tangent sphere bundles, contact structures on 3-dimensional Lie groups and a brief treatment of submanifolds. Section III will be devoted to the curvature of contact metric manifolds. Section IV will discuss complex contact manifolds and some older style topology. Section V treats curvature functionals and Ricci solitons. A sixth section has been added giving a discussion of the question of whether a Riemannian metric g can be an associated metric for more than one contact structure; at the conference this was an addendum to the third lecture.
format	article
author	Blair David E.
author_facet	Blair David E.
author_sort	Blair David E.
title	A Survey of Riemannian Contact Geometry
title_short	A Survey of Riemannian Contact Geometry
title_full	A Survey of Riemannian Contact Geometry
title_fullStr	A Survey of Riemannian Contact Geometry
title_full_unstemmed	A Survey of Riemannian Contact Geometry
title_sort	survey of riemannian contact geometry
publisher	De Gruyter
publishDate	2019
url	https://doaj.org/article/cae82b10ebb740ca8847db6055c43dd5
work_keys_str_mv	AT blairdavide asurveyofriemanniancontactgeometry AT blairdavide surveyofriemanniancontactgeometry
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A Survey of Riemannian Contact Geometry

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