Overview
- 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
Part of the book series: Infosys Science Foundation Series (ISFS)
Part of the book sub series: Infosys Science Foundation Series in Mathematical Sciences (ISFM)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
- 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
About this book
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.
Authors and Affiliations
About the authors
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.
Bibliographic Information
Book Title: Conformal Vector Fields, Ricci Solitons and Related Topics
Authors: Ramesh Sharma, Sharief Deshmukh
Series Title: Infosys Science Foundation Series
DOI: https://doi.org/10.1007/978-981-99-9258-4
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024
Hardcover ISBN: 978-981-99-9257-7Published: 20 January 2024
Softcover ISBN: 978-981-99-9260-7Due: 20 February 2024
eBook ISBN: 978-981-99-9258-4Published: 19 January 2024
Series ISSN: 2363-6149
Series E-ISSN: 2363-6157
Edition Number: 1
Number of Pages: XI, 158
Number of Illustrations: 1 b/w illustrations
Topics: Global Analysis and Analysis on Manifolds, Differential Geometry, Classical and Quantum Gravitation, Relativity Theory