Topology and Geometry of Intersections of Ellipsoids in Rn

• Verfasst von: López de Medrano, Santiago [VerfasserIn]
• Titel: Topology and Geometry of Intersections of Ellipsoids in Rn
• Verf.angabe: by Santiago López de Medrano
• Ausgabe: 1st ed. 2023.
• Verlagsort: Cham
• Verlag: Springer International Publishing
• E-Jahr: 2023
• Jahr: 2023.
• Umfang: 1 Online-Ressource (XIII, 282 p. 72 illus., 68 illus. in color.)
• Gesamttitel/Reihe: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics ; 361
• Fussnoten: Im Titel ist "n" hochgestellt
• ISBN: 978-3-031-28364-2
• DOI: doi:10.1007/978-3-031-28364-2
• Datenträger: Online-Ressource
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe: López de Medrano, Santiago: Topology and geometry of intersections of ellipsoids in Rn. - Cham, Switzerland : Springer, 2023. - xiii, 282 Seiten
• K10plus-PPN: 1846859301
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

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.

Abstract

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.