Topology and geometry of intersections of ellipsoids in Rn / Santiago López de Medrano.

Format:

Book

Author/Creator:

López de Medrano, Santiago, author.

Series:

Grundlehren der mathematischen Wissenschaften ; 361.

Grundlehren der mathematischen Wissenschaften ; 361

Language:

English

Subjects (All):

Ellipsoid.

Quadrics.

Intersection theory (Mathematics).

Physical Description:

xiii, 282 pages : illustrations (some color) ; 25 cm

Place of Publication:

Cham : Springer, 2023.

Summary:

This book gives an overview of research in the topology and geometry of intersections of quadrics in Rn, 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--back cover.

Contents:

1. Introduction

Part I. General Results : 2. General Intersections of Quadrics

3. General Operations on Intersections of Quadrics

4. Intersections of Coaxial Quadrics

5. Intersections of Coaxial Ellipsoids

Part II. Topological Description of Transverse Intersections of Concentrie Ellipsoids : 6. Characterization of Connected Sums

7. Three Coaxial Ellipsoids

8. Three Concentric Ellipsoids

9. More Than Three Coaxial Ellipsoids

10. A Family of Surfaces That Are Intersections of Concentric, Non-Coaxial Ellipsoids

Part III. Relations With Other Areas of Mathematics : 11. Dynamical Systems

12. Complex Geometry

13. Contact and Symplectic Geometry

14. Intersections with Dihedral Symmetry

15. Polyhedral Products

Part IV. Appendices : A. Proof of Theorem 2.1

B. Origins

C. Complements of Products of Spheres in Spheres

D. Diagonalizability of Matrices

References

Index.

Notes:

Includes bibliographical references (pages 275-280) and index.

ISBN:

3031283635

9783031283635

OCLC:

1369679224