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Conformal vector fields, ricci solitons and related topics

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Conformal vector fields, ricci solitons and related topics/ by Ramesh Sharma, Sharief Deshmukh.
作者:	Sharma, Ramesh.
其他作者:	Deshmukh, Sharief.
出版者:	Singapore :Springer Nature Singapore : : 2024.,
面頁冊數:	xi, 158 p. :ill., digital ;24 cm.
內容註:	1 Manifolds and Submanifolds Reviewed -- 2 Lie Group And Lie Derivative -- 3 Conformal Transformations -- 4 Conformal Vector Fields -- 5 Integral Formulas And Conformal Vector Fields.
Contained By:	Springer Nature eBook
標題:	Conformal geometry. -
電子資源:	https://doi.org/10.1007/978-981-99-9258-4
ISBN:	9789819992584

Conformal vector fields, ricci solitons and related topics
Sharma, Ramesh.

Conformal vector fields, ricci solitons and related topics[electronic resource] /by Ramesh Sharma, Sharief Deshmukh. - Singapore :Springer Nature Singapore :2024. - xi, 158 p. :ill., digital ;24 cm. - Infosys science foundation series in mathematical sciences,2364-4044. - Infosys science foundation series in mathematical sciences..

1 Manifolds and Submanifolds Reviewed -- 2 Lie Group And Lie Derivative -- 3 Conformal Transformations -- 4 Conformal Vector Fields -- 5 Integral Formulas And Conformal Vector Fields.

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.

ISBN: 9789819992584

Standard No.: 10.1007/978-981-99-9258-4doiSubjects--Topical Terms:

708569
Conformal geometry.

LC Class. No.: QA609

Dewey Class. No.: 516.36

Conformal vector fields, ricci solitons and related topics
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505 0 $a 1 Manifolds and Submanifolds Reviewed -- 2 Lie Group And Lie Derivative -- 3 Conformal Transformations -- 4 Conformal Vector Fields -- 5 Integral Formulas And Conformal Vector Fields.
520 $a 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.
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