Conformal Vector Fields, Ricci Solitons and Related Topics

Ramesh Sharma is Professor of Mathematics at the University of New Haven in Connecticut, USA, as well as Adjunct Professor at Sri Sathya Sai Institute of Higher Learning in Puttaparthi, Andhra Pradesh India. He earned his B.Sc. (Hons.) degree in 1974, M.Sc. degree in Mathematics in 1976, and his Ph.D. in Mathematics in 1980, all from Banaras Hindu University in India. He later obtained a second Ph.D. in Mathematics in 1986 from the University of Windsor in Canada. He specializes in contact, conformal, and Lorentzian geometries and has published over 100 research articles. He has also been recognized with various prestigious awards such as the Fulbright Lecturing Grant (India) in 2005, the Yale University Visiting Faculty Fellowship, and a Travel Fellowship of Connecticut Space Grant College Consortium (NASA).Sharief Deshmukh is Professor of Mathematics at King Saud University in Riyadh, Saudi Arabia. He obtained his B.Sc. and M.Sc. degrees in Mathematics from Mathwada University, India, in 1972 and 1974, respectively. He then went on to pursue his M.Phil. and Ph.D. degrees in Mathematics from Aligarh Muslim University, India, in 1978 and 1980, respectively. His research interests span a diverse range of topics in mathematics, including submanifolds, the spectrum of Riemannian manifolds, Lie groups, conformal geometry, Ricci solitons, differential equations on manifolds, and Yamabe solitons.With more than 186 research papers published in highly respected international journals, he has delivered lectures at numerous conferences and research institutions, including the Indian Institute of Technology Delhi, India, and the International Center of Theoretical Physics in Trieste, Italy. He has also supervised several M.S. theses and Ph.D. theses at King Saud University, covering various topics in differential geometry.

“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)

• 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.