Conformal Vector Fields, Ricci Solitons and Related Topics

Beschreibung

This book provides an up-to-date introduction to the theory of manifolds, submanifolds, semi-Riemannian geometry and warped product geometry, and their applications in geometry and physics. It then explores the properties of conformal vector fields and conformal transformations, including their fixed points, essentiality and the Lichnerowicz conjecture. Later chapters focus on the study of conformal vector fields on special Riemannian and Lorentzian manifolds, with a special emphasis on general relativistic spacetimes and the evolution of conformal vector fields in terms of initial data.
The book also delves into the realm of Ricci flow and Ricci solitons, starting with motivations and basic results and moving on to more advanced topics within the framework of Riemannian geometry. The main emphasis of the book is on the interplay between conformal vector fields and Ricci solitons, and their applications in contact geometry. The book highlights the fact that Nil-solitons and Sol-solitons naturally arise in the study of Ricci solitons in contact geometry. Finally, the book gives a comprehensive overview of generalized quasi-Einstein structures and Yamabe solitons and their roles in contact geometry. It would serve as a valuable resource for graduate students and researchers in mathematics and physics as well as those interested in the intersection of geometry and physics.
This book provides an up-to-date introduction to the theory of manifolds, submanifolds, semi-Riemannian geometry and warped product geometry, and their applications in geometry and physics. It then explores the properties of conformal vector fields and conformal transformations, including their fixed points, essentiality and the Lichnerowicz conjecture. Later chapters focus on the study of conformal vector fields on special Riemannian and Lorentzian manifolds, with a special emphasis on general relativistic spacetimes and the evolution of conformal vector fields in terms of initial data.
The book also delves into the realm of Ricci flow and Ricci solitons, starting with motivations and basic results and moving on to more advanced topics within the framework of Riemannian geometry. The main emphasis of the book is on the interplay between conformal vector fields and Ricci solitons, and their applications in contact geometry. The book highlights the fact that Nil-solitons and Sol-solitons naturally arise in the study of Ricci solitons in contact geometry. Finally, the book gives a comprehensive overview of generalized quasi-Einstein structures and Yamabe solitons and their roles in contact geometry. It would serve as a valuable resource for graduate students and researchers in mathematics and physics as well as those interested in the intersection of geometry and physics.

Masters manifold theory, conformal transformations, and Ricci solitons to enhance your skills in geometry and physics Discovers the interplay between conformal vector fields and Ricci solitons and their roles in contact geometry Gains a comprehensive understanding of generalized quasi-Einstein structures and Yamabe solitons in contact geometry

Autor*in

Ramesh Sharma

Themen in »Conformal Vector Fields, Ricci Solitons and Related Topics«

Submanifolds Lie Group Conformal Vector Fields Quasi-Einstein Manifolds Riemannian and Lorentzian Geometrie Lie Derivative Conformal Transformations Lorentzian Manifolds Complex and Contact Geometries Contact Riemannian Manifolds Ricci Solitons Semi-Riemannian Geometry Space-times of General Relativity

Stimmen zu »Conformal Vector Fields, Ricci Solitons and Related Topics«

“This book provides a comprehensive study of conformal vector fields, Ricci solitons, and their applications in differential geometry and mathematical physics. Bridging classical differential geometry with modern research topics, it serves as a valuable resource for both students and researchers. The text is well structured, introducing fundamental mathematical preliminaries before progressing to advanced topics such as Ricci solitons, quasi-Einstein manifolds, and Yamabe solitons.” (Sameh Shenawy, Mathematical Reviews, May, 2025)

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