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The Geometry of Hessian Structures

✍ Scribed by Hirohiko Shima

Book ID
127449063
Publisher
World Scientific
Year
2007
Tongue
English
Weight
1 MB
Category
Library
City
Hackensack, N.J
ISBN
9812707530

No coin nor oath required. For personal study only.

✦ Synopsis

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.

✦ Subjects

Дифференциальная геометрия и топология

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The geometry of Hessian structures
The geometry of Hessian structures
✍ Hirohiko Shima 📂 Library 📅 2007 🏛 World Scientific 🌐 English ⚖ 1 MB

The geometry of Hessian structures is a fascinating emerging field of research connected with many important pure mathematical branches such as affine differential geometry, homogeneous spaces and cohomology. This systematic introduction to the subject first develops the fundamentals of Hessian stru

Geometry of Hessian manifolds
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✍ Hirohiko Shima; Katsumi Yagi 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 906 KB

Let M be an aftine manifold with a flat affme connection D. A Riemannian metric g on M is said to be a Hessian metric if g has a local expression g = D'u. A manifold M provided with such a pair (D, g) is called a Hessian manifold. We first prove the convexity of a Hessian manifold. We give a Weitzen