Topology and geometry of intersections of ellipsoids in R^n / Santiago López de Medrano.
López de Medrano, Santiago.
2023
QA561
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Title Topology and geometry of intersections of ellipsoids in R^n / Santiago López de Medrano.
Author López de Medrano, Santiago.
ISBN 9783031283642 (electronic bk.)
3031283643 (electronic bk.)
3031283635
9783031283635
DOI https://doi.org/10.1007/978-3-031-28364-2
Imprint Cham : Springer, 2023.
Language English
Description 1 online resource (277 p.).
Other Standard Identifiers 10.1007/978-3-031-28364-2 doi
Call Number QA561
Dewey Decimal Classification 516.3
Summary This book gives an overview of research in the topology and geometry of intersections of quadrics in $\mathbb{R}^n$, with a focus on intersections of concentric ellipsoids and related spaces. Unifying and organizing material previously spread over many articles, it also contains new results. The first part provides very detailed foundations of a wide-ranging theory that could be useful for future developments. It includes chapters on general intersections of quadrics, operations on them, and intersections of concentric and coaxial quadrics. Moving from the general to the specific, the second part focuses on a topological description of transverse intersections of concentric ellipsoids, including a complete description of the case of three ellipsoids, and of some large families of more than three of them. The third part looks at relations to other areas of mathematics such as dynamical systems, complex geometry, contact and symplectic geometry, and other applications. An appendix gathers some technical items and also gives an account of the origins, motivations and progression of the subject, including historical recollections of the author, who has been central to its development.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed June 5, 2023).
Series Grundlehren der mathematischen Wissenschaften ; 361.
Available in Other Form Topology and Geometry of Intersections of Ellipsoids in R^n
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1 Introduction
PART I: General Results
2 General intersections of quadrics
3 Intersections of coaxial quadrics
4 Intersections of coaxial ellipsoids
PART II: Topological description of transverse intersections of concentric ellipsoids
5 Characterization of connected sums
6 Three coaxial ellipsoids
7 Three concentric ellipsoids
8 More than three coaxial ellipsoids
9 A family of surfaces that are intersections of concentric, non-coaxial, ellipsoid
PART III: Relations with other areas of Mathematics
10 Dynamical systems
11 Complex Geometry
12 Contact and symplectic Geometry
13 Intersections with dihedral symmetry
14 Toric Topology and polyhedral products
PART IV: Appendices
15 Appendix 1. Proof of Theorem 2.1
16 Appendix 2. Origins
17 Appendix 3. Diagonalizability of matrices
18 Appendix 4: Complements of products of spheres in spheres.

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