This book, Complex Geometry and Mathematical Physics: Lorentzian Geometry and Field Equations (Book III-A), presents results from Lorentzian geometry (causality theory of spacetimes, submanifolds of Lorentzian manifolds, compact Lorentzian holonomy) and general relativity and gravitation theory. The first in a captivating series of three books, it demonstrates the bond between physics and geometry such as the mathematical structure of Maxwell’s equations predicting Minkowskian geometry, geodesic motion in the Newtonian limit, Kepler’s problem and Mercury’s perihelic shift, Morse theory for light rays). The book also includes discussion on certain quantum mechanical aspects (bending of light in quantum gravity) and the structure of Einstein’s (linearized) field equations in empty space or in the presence of matter. The other two books of the series are:
Complex Geometry and Mathematical Physics: Classical and Quantum Singularities of Space-Times (Book III-B)
Complex Geometry and Mathematical Physics: Complex Analysis versus General Relativity Theory (Book III-C)
"Complex Geometry and Mathematical Physics" is part of the ampler book project "Differential Geometry, Partial Differential Equations and Mathematical Physics" by the same Authors, and aims to demonstrate the interaction between complex analysis and complex geometry on one hand, and general relativity and (quantum) gravity theory on the other, with an emphasis on the modern and contemporary trends of applying ideas from GRG theory to certain problems arising in complex analysis, such as the many pathologies of the Diederich–Fornæss worm domains.
Table of Contents:
Chapter 1. Lorentzian geometry.- Chapter 2. Physics and Geometry.- Chapter 3. Linearized eld equations.- Chapter 4. Field Equations for Nonempty Space.
About the Author :
Elisabetta Barletta is Professor of mathematical analysis at the Department of Mathematics, Computer Science and Economy, Universit a degli Studi della Basilicata (Potenza, Italy). She joined the university as Lecturer in 1979, then became Associate Professor in 2003. She visited several institutes worldwide: Visiting Fellow at the University of Maryland (U.S.A.), from 1982-1983, to conduct research with Carlos A. Berenstein; Visiting Fellow at Indiana University (U.S.A.), from 1987-1988, to do research with Eric Bedford; and Visiting Professor at Tohoku University (Japan), in 2003, invited by Seiki Nishikawa. Her research interests include complex analysis of functions of several complex variables, reproducing kernel Hilbert spaces, the geometry of Levi at Cauchy-Riemann manifolds and proper holomorphic maps of pseudoconvex domains.
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 are in the study of the tangential Cauchy-Riemann (CR) 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. With more than 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 former 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, from 2001-2006. He earned his Ph.D. degree from Aligarh Muslim University (Aligarh, India), in 1988. His areas of research are the geometry of CR-submanifolds, Riemannian submersions and tangent bundles. Author of more than 60 research papers, he has visited several world universities including, but not limited to, the University of Patras (Greece) (from 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 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 and applications of differential geometry in physics. With more than 54 research papers to his credit and coedited 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), Mohammad Hasan 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.
