Read Aspects of Differential Geometry IV

Aspects of Differential Geometry IV

Unknown Author

4.9/5 (11951 ratings)

Description: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 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.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Aspects of Differential Geometry IV. To get started finding Aspects of Differential Geometry IV, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

Pages: 167

Format: PDF, EPUB & Kindle Edition

Publisher: Morgan & Claypool

Release: 2019

ISBN: 1681735644

Description: 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 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.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Aspects of Differential Geometry IV. To get started finding Aspects of Differential Geometry IV, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

Special Offer | $0.00

Special Offer! | $0.00

Aspects of Differential Geometry IV

Aspects of Differential Geometry IV

More Books