The Geometry of Hessian Structures

Download or read book The Geometry of Hessian Structures written by Hirohiko Shima and published by World Scientific. This book was released on 2007 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: The geometry of Hessian structures is a fascinating emerging field of research. It is in particular a very close relative of Knhlerian 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 theory."