Name: Aspects of Differential Geometry IV (en Inglés)
Price: 360.42 PEN
Availability: InStock
Author: Calviño-Louzao, Esteban ; García-Río, Eduardo ; Gilkey, Peter
ISBN: 9783031012884

portada Aspects of Differential Geometry IV (en Inglés)

Formato

Libro Físico

Autor

Peter Gilkey

Eduardo Garcia-Rio

Esteban Calviño-Louzao

Editorial

Springer

Idioma

Inglés

N° páginas

149

Encuadernación

Tapa Blanda

ISBN13

9783031012884

N° edición

Categorías

Cálculo diferencial y ecuaciones
Geometría diferencial y riemanniana
Probabilidad y estadística

Aspects of Differential Geometry IV (en Inglés)

Peter Gilkey (Autor) · Eduardo Garcia-Rio (Autor) · Esteban Calviño-Louzao (Autor) · Springer · Tapa Blanda

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S/ 720,84

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Reseña del libro "Aspects of Differential Geometry IV (en Inglés)"

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 ℝ is Abelian and the �� + �� group\index{ax+b 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 ℝ . 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 �� . 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.