Geometry of Cauchy-Riemann Submanifolds

This book gathers contributions by respected experts on the theory of isometric immersions between Riemannian manifolds, and focuses on the geometry of CR structures on submanifolds in Hermitian manifolds. CR structures are a bundle theoretic recast of the tangential CauchyRiemann equations in complex analysis involving several complex variables. The book covers a wide range of topics such as Sasakian geometry, Kaehler and locally conformal Kaehler geometry, the tangential CR equations, Lorentzian geometry, holomorphic statistical manifolds, and paraquaternionic CR submanifolds.Intended as a tribute to Professor Aurel Bejancu, who discovered the notion of a CR submanifold of a Hermitian manifold in 1978, the book provides an up-to-date overview of several topics in the geometry of CR submanifolds. Presenting detailed information on the most recent advances in the area, it represents a useful resource for mathematicians and physicists alike.

Presents a collection of reports on the most recent results on CR submanifolds in various ambient spaces Explores the applications of CR geometry, and in particular the theory of CR submanifolds, to other scientific areas Attempts to fill in the gap between the geometry of the second fundamental form of a CR submanifold and the more mathematical analysis oriented aspects of CR geometry Pays a tribute to Professor Aurel Bejancu, the 1978 discoverer of the notion of a CR submanifold of a Hermitian manifold Includes supplementary material: sn.pub/extras

Auteur

Sorin Dragomir is professor of mathematical analysis at the Università degli Studi della Basilicata (Potenza, Italy). He studied mathematics at the Universitatea din Bucureti (Bucharest) under S. Ianu, D. Smaranda, I. Colojoar, M. Jurchescu and K. Teleman, and earned his Ph.D. at Stony Brook University (New York) in 1992 under Denson C. Hill. His research interests concern the study of the tangential CauchyRiemann equations, the interplay between the Kählerian geometry of pseudoconvex domains and the pseudohermitian geometry of their boundaries, the impact of subelliptic theory on CR geometry, the applications of CR geometry to spacetime physics. He authored over 140 research papers and 4 monographs. His wider interests regard the development and dissemination of both western and eastern mathematical sciences. An Italian citizen since 1991, he was born in Romania, and has solid cultural roots in Romanian mathematics, while his mathematical orientation over the last 10 years strongly owes to H. Urakawa (Sendai, Japan), E. Lanconelli (Bologna, Italy), J.P. D'Angelo (Urbana-Champaign, U.S.A.) and H. Jacobowitz (Camden, U.S.A.). He is member of Unione Matematica Italiana, American Mathematical Society, and Mathematical Society of Japan.

Mohammad Hasan Shahid is professor at the Department of Mathematics, Jamia Millia Islamia, New Delhi, India. He also served King Abdul Aziz University, Jeddah, Kingdom of Saudi Arabia, as associate professor during 20012006. He earned his PhD degree at Aligarh Muslim University, India, in 1988. His areas of research are the geometry of CR- submanifolds, Riemannian submersions and tangent bundles. Author of over 60 research papers, he has visited several world universities including, but not limited to, the University of Patras, Greece, (during 19971998) under postdoctoral scholarship from State Scholarship Foundation, Greece; the University of Leeds, England (in 1992) to deliver lectures; Ecole Polytechnique, Paris (in 2015); Universite De Montpellier, France (in 2015); and Universidad De Sevilla, Spain (in 2015). He is member of the Industrial Mathematical Society and the Indian Association for General Relativity.

Falleh R. Al-Solamy is professor of differential geometry at King Abdulaziz University (Jeddah, Saudi Arabia). He studied mathematics at King Abdulaziz University (Jeddah, Saudi Arabia) and earned his Ph.D. at the University of Wales Swansea (Swansea, U.K.) in 1998 under Edwin Beggs. His research interests concern the study of the geometry of submanifolds in Riemannian and semi-Riemannian manifolds, Einstein manifolds, applications of differential geometry in physics. He authored 54 research papers and co/edited 1 book titled, Fixed Point Theory, Variational Analysis, and Optimization. His mathematical orientation over the last 10 years strongly owes to S. Deshmukh (Riyadh, Saudi Arabia), M.H. Shahid (New Delhi, India) andV.A. Khan (Aligarh, India). He is member of the London Mathematical Society, the Institute of Physics, the Saudi Association for Mathematical Sciences, the Tensor Society, the Saudi Computer Society and the American Mathematical Society.

Contenu

Chapter 1. CR-warped submanifolds in Kaehler manifolds.- Chapter 2. CR Submanifolds and -invariants.- Chapter 3. CR Submanifolds of the nearly Kahler 6-sphere.- Chapter 4. CR submanifolds of Hermitian manifolds and the tangential C-R equations.- Chapter 5. CR Submanifolds in (l.c.a.) Kaehler and S-manifolds.- Chapter 6. Lorentzian geometry and CR submanifolds.- Chapter 7. Submanifolds in holomorphic statistical manifolds.- Chapter 8. CR Submanifolds in complex and Sasakian space forms.- Chapter 9. CR-Doubly warped product submanifolds.- Chapter 10. Ideal CR submanifolds.- Chapter 11. Submersions of CR submanifolds.- Chapter 12. CR Submanifolds of semi-Kaehler manifolds.- Chapter 13. Paraquaternionic CR submanifolds.