© 2016

Geometry of Cauchy-Riemann Submanifolds

  • Sorin Dragomir
  • Mohammad Hasan Shahid
  • Falleh R. Al-Solamy

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Bang-Yen Chen
    Pages 27-55
  3. Miroslava Antić, Luc Vrancken
    Pages 57-90
  4. Elisabetta Barletta, Sorin Dragomir
    Pages 91-122
  5. José Luis Cabrerizo, Alfonso Carriazo, Luis M. Fernández
    Pages 123-150
  6. Krishan L. Duggal
    Pages 151-177
  7. Hitoshi Furuhata, Izumi Hasegawa
    Pages 179-215
  8. Adela Mihai, Ion Mihai
    Pages 217-266
  9. Andreea Olteanu
    Pages 267-288
  10. Toru Sasahara
    Pages 289-310
  11. Mohammad Hasan Shahid, Falleh R. Al-Solamy, Mohammed Jamali
    Pages 311-342
  12. Gabriel-Eduard Vîlcu
    Pages 361-390

About this book


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 Cauchy–Riemann 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.


CR-submanifolds Kaehler manifold Sasakian manifolds Cauchy–Riemann structure Semi-Riemannian submersions Differential geometry Riemannian geometry

Editors and affiliations

  • Sorin Dragomir
    • 1
  • Mohammad Hasan Shahid
    • 2
  • Falleh R. Al-Solamy
    • 3
  1. 1.Dipartimento di Matematica e InformaticaUniversità degli Studi della BasilicataPotenzaItaly
  2. 2.Dept. of Maths., Faculty of Natural SciJamia Millia Islamia,New DelhiIndia
  3. 3.Department of MathematicsKing Abdul Aziz UniversityThuwalSaudi Arabia

About the editors

Sorin Dragomir is professor of mathematical analysis at the Università degli Studi della Basilicata (Potenza, Italy). He studied mathematics at the Universitatea din Bucureşti (Bucharest) under S. Ianuş, D. Smaranda, I. Colojoară, 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 Cauchy–Riemann 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 space–time 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 2001–2006. 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 1997–1998) 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) and V.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.

Bibliographic information