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

• Autore: Shima Hirohiko
• Pubblicazione: Singapore ; ; Hackensack, N.J., : World Scientific, c2007
• Descrizione fisica: 1 online resource (261 p.)
• Disciplina: 516.36
• Soggetto topico: Geometry, Differential; Homology theory; Homogeneous spaces; Manifolds (Mathematics)
• 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
• Altri titoli varianti: Hessian structures
• Titolo autorizzato: Geometry of Hessian structures
• ISBN: 1-281-12108-8; 9786611121082; 981-270-753-0
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910784038503321
• Lo trovi qui: Univ. Federico II