Geometry Of Hessian Structures, The - Tapa dura

The book is clearly and very rigorously written. The author manages to present the geometry of Hessian structures as a fascinating field of research. I consider it as an excellent instrument for the specialists in the field. -- Zentralblatt MATH "Zentralblatt MATH" The book is a good, well-written overview of Hessian structures from the point of view of classical differential geometry. -- Mathematical Reviews "Mathematical Reviews"

The geometry of Hessian structures is a fascinating emerging field of research. It is in particular a very close relative of Kahlerian 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.