Aspects of Differential Geometry IV (Synthesis Lectures on Mathematics and Statistics, 26)
by Calviño-Louzao, Esteban; García-Río, Eduardo; Gilkey, Peter
- New
- Paperback
- Condition
- New
- ISBN 10
- 1681735636
- ISBN 13
- 9781681735634
- Seller
-
Kraków, Poland
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About This Item
Morgan & Claypool Publishers, 2019 8vo (23.5 cm), XVII, 149 pp. Laminated wrappers. Synopsis: Book IV continues the discussion begun in the first three volumes. Although it is aimed at first-year graduate students, it is also intended to serve as a basic reference for people working in affine differential geometry. It also should be accessible to undergraduates interested in affine differential geometry. We are primarily concerned with the study of affine surfaces which are locally homogeneous. We discuss affine gradient Ricci solitons, affine Killing vector fields, and geodesic completeness. Opozda has classified the affine surface geometries which are locally homogeneous; we follow her classification. Up to isomorphism, there are two simply connected Lie groups of dimension 2. The translation group ℝ² is Abelian and the ???? + ?? group is non-Abelian. The first chapter presents foundational material. The second chapter deals with Type ?? surfaces. These are the left-invariant affine geometries on ℝ². Associating to each Type ?? surface the space of solutions to the quasi-Einstein equation corresponding to the eigenvalue ?? = -1 turns out to be a very powerful technique and plays a central role in our study as it links an analytic invariant with the underlying geometry of the surface. The third chapter deals with Type ?? surfaces; these are the left-invariant affine geometries on the ???? + ?? group. These geometries form a very rich family which is only partially understood. The only remaining homogeneous geometry is that of the sphere ??². The fourth chapter presents relations between the geometry of an affine surface and the geometry of the cotangent bundle equipped with the neutral signature metric of the modified Riemannian extension.
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Details
- Bookseller
- Leopolis Volodymyr Dmyterko (PL)
- Bookseller's Inventory #
- 008461
- Title
- Aspects of Differential Geometry IV (Synthesis Lectures on Mathematics and Statistics, 26)
- Author
- Calviño-Louzao, Esteban; García-Río, Eduardo; Gilkey, Peter
- Format/Binding
- Soft cover
- Book Condition
- New New
- Quantity Available
- 1
- Binding
- Paperback
- ISBN 10
- 1681735636
- ISBN 13
- 9781681735634
- Publisher
- Morgan & Claypool Publishers
- Date Published
- 2019
- Bookseller catalogs
- Mathematics;
- Note
- May be a multi-volume set and require additional postage.
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Leopolis Volodymyr Dmyterko
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About the Seller
Leopolis Volodymyr Dmyterko
Biblio member since 2019
Kraków
About Leopolis Volodymyr Dmyterko
Specializing in mathematical sciences, Church Slavonic and Slavic books, Eastern European history, travels and topography, bibliography, history and art of the book, history of libraries and collections
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- Wrappers
- The paper covering on the outside of a paperback. Also see the entry for pictorial wraps, color illustrated coverings for...