03405nam a22004815i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001700153072001600170072002300186072001500209100007700224245012500301250001800426264007200444300004200516336002600558337002600584338003600610347002400646490007500670505018800745520139700933650003502330650002902365650002802394650003402422650004702456650002702503650002402530700008002554710003402634773002602668776003602694776003602730776003602766830007502802856004602877978-981-99-9258-4DE-He21320251030111358.0cr nn 008mamaa240119s2024    si |    s    |||| 0|eng d  a97898199925847 a10.1007/978-981-99-9258-42doi 4aQA614-614.97 7aPBK2bicssc 7aMAT0340002bisacsh 7aPBK2thema1 aSharma, Ramesh.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aConformal Vector Fields, Ricci Solitons and Related Topicsh[electronic resource] /cby Ramesh Sharma, Sharief Deshmukh.  a1st ed. 2024. 1aSingapore :bSpringer Nature Singapore :bImprint: Springer,c2024.  aXI, 158 p. 1 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aInfosys Science Foundation Series in Mathematical Sciences,x2364-40440 a1 Manifolds and Submanifolds Reviewed -- 2 Lie Group And Lie Derivative -- 3 Conformal Transformations -- 4 Conformal Vector Fields -- 5 Integral Formulas And Conformal Vector Fields.  aThis 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. 0aGlobal analysis (Mathematics). 0aManifolds (Mathematics). 0aGeometry, Differential. 0aGeneral relativity (Physics).14aGlobal Analysis and Analysis on Manifolds.24aDifferential Geometry.24aGeneral Relativity.1 aDeshmukh, Sharief.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978981999257708iPrinted edition:z978981999259108iPrinted edition:z9789819992607 0aInfosys Science Foundation Series in Mathematical Sciences,x2364-404440uhttps://doi.org/10.1007/978-981-99-9258-4