The geometry of Hessian structures / Hirohiko Shima.

Format:

Book

Author/Creator:

Shima, Hirohiko.

Language:

English

Subjects (All):

Geometry, Differential.

Homology theory.

Homogeneous spaces.

Manifolds (Mathematics).

Physical Description:

1 online resource (261 p.)

Edition:

1st ed.

Other Title:

Hessian structures

Place of Publication:

Singapore ; Hackensack, N.J. : World Scientific, c2007.

Language Note:

English

Summary:

The geometry of Hessian structures is a fascinating emerging field of research. It is in particular a very close relative of Kählerian geometry, and connected with many important pure mathematical branches such as affine differential geometry, homogeneous spaces and cohomology. The theory also finds deep relation to information geometry in applied mathematics. This systematic introduction to the subject first develops the fundamentals of Hessian structures on the basis of a certain pair of a flat connection and a Riemannian metric, and then describes these related fields as applications of the

Contents:

Preface; Introduction; Contents; 1. Affine spaces and connections; 2. Hessian structures; 3. Curvatures for Hessian structures; 4. Regular convex cones; 5. Hessian structures and affine differential geometry; 6. Hessian structures and information geometry; 7. Cohomology on at manifolds; 8. Compact Hessian manifolds; 9. Symmetric spaces with invariant Hessian structures; 10. Homogeneous spaces with invariant Hessian structures; 11. Homogeneous spaces with invariant projectively at connections; Bibliography; Index

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 237-241) and index.

ISBN:

9786611121082

9781281121080

1281121088

9789812707536

9812707530

OCLC:

476099460