Articoli correlati a Aspects of Differential Geometry (4)
Sinossi
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.
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
- EditoreMorgan & Claypool
- Data di pubblicazione2019
- ISBN 10 1681735652
- ISBN 13 9781681735658
- RilegaturaCopertina rigida
- LinguaInglese
- Numero di pagine167
- Contatto del produttorenon disponibile
Compra nuovo
Visualizza questo articolo
EUR 38,33
EUR 17,62 per la spedizione da Regno Unito a Italia
Destinazione, tempi e costiAltre edizioni note dello stesso titolo
Risultati della ricerca per Aspects of Differential Geometry (4)
Foto dell'editore
Aspects of Differential Geometry IV (Synthesis Lectures on Mathematics and Statistics)
Da: Karl Eynon Books Ltd, Tywyn, Regno Unito
Valutazione del venditore 5 su 5 stelle
Hardback. Condizione: New. new copies no faults. 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. Codice articolo 103388
Quantità: 1 disponibili