Ricci Solitons in Low Dimensions - Couverture souple

Chow, Bennett

Couverture souple

ISBN 10 : 1470475235 ISBN 13 : 9781470475239

Editeur : American Mathematical Society, 2023

Synopsis

Ricci flow is an exciting subject of mathematics with diverse applications in geometry, topology, and other fields. It employs a heat-type equation to smooth an initial Riemannian metric on a manifold. The formation of singularities in the manifold's topology and geometry is a desirable outcome. Upon closer examination, these singularities often reveal intriguing structures known as Ricci solitons.

This introductory book focuses on Ricci solitons, shedding light on their role in understanding singularity formation in Ricci flow and formulating surgery-based Ricci flow, which holds potential applications in topology. Notably successful in dimension 3, the book narrows its scope to low dimensions: 2 and 3, where the theory of Ricci solitons is well established. A comprehensive discussion of this theory is provided, while also establishing the groundwork for exploring Ricci solitons in higher dimensions.

A particularly exciting area of study involves the potential applications of Ricci flow in comprehending the topology of 4-dimensional smooth manifolds. Geared towards graduate students who have completed a one-semester course on Riemannian geometry, this book serves as an ideal resource for related courses or seminars centered on Ricci solitons.

A propos du livre

À propos de l'auteur

Bennett Chow, University of California, San Diego, La Jolla, CA.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2023
• Langue: anglais
• ISBN 10: 1470475235
• ISBN 13: 9781470475239
• Reliure: Broché
• Nombre de pages: 339
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible