02998nam 2200649Ia 450 991078403850332120230721025415.01-281-12108-89786611121082981-270-753-0(CKB)1000000000334189(EBL)312289(OCoLC)476099460(SSID)ssj0000162065(PQKBManifestationID)11947043(PQKBTitleCode)TC0000162065(PQKBWorkID)10200863(PQKB)11585512(MiAaPQ)EBC312289(WSP)00006241(Au-PeEL)EBL312289(CaPaEBR)ebr10188822(CaONFJC)MIL112108(OCoLC)172989118(EXLCZ)99100000000033418920070428d2007 uy 0engur|n|---|||||txtccrThe geometry of Hessian structures[electronic resource] /Hirohiko ShimaSingapore ;Hackensack, N.J. World Scientificc20071 online resource (261 p.)Description based upon print version of record.981-270-031-5 Includes bibliographical references (p. 237-241) and index.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; IndexThe 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 theHessian structuresGeometry, DifferentialHomology theoryHomogeneous spacesManifolds (Mathematics)Geometry, Differential.Homology theory.Homogeneous spaces.Manifolds (Mathematics)516.36Shima Hirohiko629790MiAaPQMiAaPQMiAaPQBOOK9910784038503321Geometry of Hessian structures1225626UNINA