1.

Record Nr.

UNINA9910784038503321

Autore

Shima Hirohiko

Titolo

The geometry of Hessian structures [[electronic resource] /] / Hirohiko Shima

Pubbl/distr/stampa

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

ISBN

1-281-12108-8

9786611121082

981-270-753-0

Descrizione fisica

1 online resource (261 p.)

Disciplina

516.36

Soggetti

Geometry, Differential

Homology theory

Homogeneous spaces

Manifolds (Mathematics)

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

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

Nota di contenuto

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

Sommario/riassunto

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