國立高雄大學圖資館 |

Conformal vector fields, ricci solitons and related topics

Record Type:	Electronic resources : Monograph/item
Title/Author:	Conformal vector fields, ricci solitons and related topicsby Ramesh Sharma, Sharief Deshmukh.
Author:	Sharma, Ramesh.
other author:	Deshmukh, Sharief.
Published:	Singapore :Springer Nature Singapore :2024.
Description:	xi, 158 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Conformal geometry.
Online resource:	https://doi.org/10.1007/978-981-99-9258-4
ISBN:	9789819992584$q(electronic bk.)

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$q(electronic bk.)

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

468280
Conformal geometry.

LC Class. No.: QA609

Dewey Class. No.: 516.36

Conformal vector fields, ricci solitons and related topics
LDR:02656nmm a2200337 a 4500 001 663409
003 DE-He213
005 20240119213258.0
006 m d
007 cr nn 008maaau
008 241203s2024 si s 0 eng d
020 $a 9789819992584$q(electronic bk.)
020 $a 9789819992577$q(paper)
024 7 $a 10.1007/978-981-99-9258-4 $2 doi
035 $a 978-981-99-9258-4
040 $a GP $c GP
041 0 $a eng
050 4 $a QA609
072 7 $a PBK $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBK $2 thema
082 0 4 $a 516.36 $2 23
090 $a QA609 $b .S531 2024
100 1 $a Sharma, Ramesh. $3 770684
245 1 0 $a Conformal vector fields, ricci solitons and related topics $h [electronic resource] / $c by Ramesh Sharma, Sharief Deshmukh.
260 $a Singapore : $b Springer Nature Singapore : $b Imprint: Springer, $c 2024.
300 $a xi, 158 p. : $b ill., digital ; $c 24 cm.
490 1 $a Infosys science foundation series in mathematical sciences, $x 2364-4044
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.
650 0 $a Conformal geometry. $3 468280
650 0 $a Manifolds (Mathematics) $3 198996
650 0 $a Ricci flow. $3 359870
650 1 4 $a Global Analysis and Analysis on Manifolds. $3 273786
650 2 4 $a Differential Geometry. $3 273785
650 2 4 $a General Relativity. $3 920214
700 1 $a Deshmukh, Sharief. $3 975684
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Infosys science foundation series in mathematical sciences. $3 825969
856 4 0 $u https://doi.org/10.1007/978-981-99-9258-4
950 $a Mathematics and Statistics (SpringerNature-11649)