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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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2019-01-01
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| Series: | Complex Manifolds |
| Online Access: | https://doi.org/10.1515/coma-2019-0002 |
| _version_ | 1818834652294545408 |
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| author | Blair David E. |
| author_facet | Blair David E. |
| author_sort | Blair David E. |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-19T02:38:13Z |
| format | Article |
| id | doaj.art-cae82b10ebb740ca8847db6055c43dd5 |
| institution | Directory Open Access Journal |
| issn | 2300-7443 |
| language | English |
| last_indexed | 2024-12-19T02:38:13Z |
| publishDate | 2019-01-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Complex Manifolds |
| spelling | doaj.art-cae82b10ebb740ca8847db6055c43dd52022-12-21T20:39:17ZengDe GruyterComplex Manifolds2300-74432019-01-0161316410.1515/coma-2019-0002coma-2019-0002A Survey of Riemannian Contact GeometryBlair David E.0Department of Mathematics, Michigan State University,East Lansing, USAThis 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.https://doi.org/10.1515/coma-2019-0002 |
| spellingShingle | Blair David E. A Survey of Riemannian Contact Geometry Complex Manifolds |
| title | 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_short | A Survey of Riemannian Contact Geometry |
| title_sort | survey of riemannian contact geometry |
| url | https://doi.org/10.1515/coma-2019-0002 |
| work_keys_str_mv | AT blairdavide asurveyofriemanniancontactgeometry AT blairdavide surveyofriemanniancontactgeometry |