Grassmann and Stiefel Varieties over Composition Algebras (Rsme Springer Series) （2023）

Golasiński, Marek/ Gómez Ruiz, Francisco

Springer International Publishing AG（2024/08発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 334 p.
• 言語 ENG
• 商品コード 9783031364075

Full Description

This monograph deals with matrix manifolds, i.e., manifolds for which there is a natural representation of their elements as matrix arrays. Classical matrix manifolds (Stiefel, Grassmann and flag manifolds) are studied in a more general setting. It provides tools to investigate matrix varieties over Pythagorean formally real fields. The presentation of the book is reasonably self-contained. It contains a number of nontrivial results on matrix manifolds useful for people working not only in differential geometry and Riemannian geometry but in other areas of mathematics as well. It is also designed to be readable by a graduate student who has taken introductory courses in algebraic and differential geometry.

Contents

- 1. Algebraic Preliminaries. - 2. Exceptional Groups .G2(K) and .F4(K). - 3. Stiefel, Grassmann Manifolds and Generalizations. - 4. More Classical Matrix Varieties. - 5. Algebraic Generalizations of Matrix Varieties. - 6. Curvature, Geodesics and Distance on Matrix Varieties.