Locally Conformal Kähler Geometry

. E C, 0 '1 . be the O-dimensional Lie n group generated by the transformation z ~ >.z, z E C - {a}. Then (cf.

Autorentext

Elisabetta Barletta is Associate Professor of Mathematical Analysis at the Department of Mathematics, Computer Science and Economy, Università degli Studi della Basilicata (Potenza, Italy). She studied mathematics at Università di Firenze, obtaining her degree in mathematics in 1979, under Giuseppe Tomassini. Assistant Professor at Università della Basilicata since 1986, she became Associate Professor in 2003. Visiting Fellow at the University of Maryland, USA (1982-1983, working with Carlos A. Berenstein); Visiting Fellow at Indiana University, USA (1987-1988, working with Eric Bedford); Visiting Professor at Tohoku University, Japan, (2003, invited by Seiki Nishikawa). Author of over 60 research papers and of the AMS Monograph Foliations in Cauchy-Riemann geometry (2007), her research interests include complex analysis of functions of several complex variables, reproducing kernel Hilbert spaces, the geometry of Levi flat 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 Bucure ti, Bucharest, under S. Ianü, 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 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. 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 to 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 100 research papers and three contributed volumes published in Springer, he has visited several world universities including, but not limited to, the University of Patras (Greece) (from 1997 to 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, UK), 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,

Klappentext

. E C, 0 '1 . be the O-dimensional Lie n group generated by the transformation z ~ >.z, z E C - {a}. Then (cf.

Inhalt
1 L.c.K. Manifolds.- 2 Principally Important Properties.- 2.1 Vaisman's conjectures.- 2.2 Reducible manifolds.- 2.3 Curvature properties.- 2.4 Blow-up.- 2.5 An adapted cohomology.- 3 Examples.- 3.1 Hopf manifolds.- 3.2 The Inoue surfaces.- 3.3 A generalization of Thurston's manifold.- 3.4 A four-dimensional solvmanifold.- 3.5 SU(2) x S1.- 3.6 Noncompact examples.- 3.7 Brieskorn & Van de Ven's manifolds.- 4 Generalized Hopf manifolds.- 5 Distributions on a g.H. manifold.- 6 Structure theorems.- 6.1 Regular Vaisman manifolds.- 6.2 L.c.K.0 manifolds.- 6.3 A spectral characterization.- 6.4 k-Vaisman manifolds.- 7 Harmonic and holomorphic forms.- 7.1 Harmonic forms.- 7.2 Holomorphic vector fields.- 8 Hermitian surfaces.- 9 Holomorphic maps.- 9.1 General properties.- 9.2 Pseudoharmonic maps.- 9.3 A Schwarz lemma.- 10 L.c.K. submersions.- 10.1 Submersions from CH?n.- 10.2 L.c.K. submersions.- 10.3 Compact total space.- 10.4 Total space a g.H. manifold.- 11 L.c. hyperKähler manifolds.- 12 Submanifolds.- 12.1 Fundamental tensors.- 12.2 Complex and CR submanifolds.- 12.3 Anti-invariant submanifolds.- 12.4 Examples.- 12.5 Distributions on submanifolds.- 12.6 Totally umbilical submanifolds.- 13 Extrinsic spheres.- 13.1 Curvature-invariant submanifolds.- 13.2 Extrinsic and standard spheres.- 13.3 Complete intersections.- 13.4 Yano's integral formula.- 14 Real hypersurfaces.- 14.1 Principal curvatures.- 14.2 Quasi-Einstein hypersurfaces.- 14.3 Homogeneous hypersurfaces.- 14.4 Type numbers.- 14.5 L. c. cosymplectic metrics.- 15 Complex submanifolds.- 15.1 Quasi-Einstein submanifolds.- 15.2 The normal bundle.- 15.3 L.c.K. and Kähler submanifolds.- 15.4 A Frankel type theorem.- 15.5 Planar geodesic immersions.- 16 Integral formulae.- 16.1 Hopf fibrations.- 16.2 The horizontallifting technique.- 16.3 The main result.- 17 Miscellanea.- 17.1 Parallel IInd fundamental form.- 17.2 Stability.- 17.3 f-Structures.- 17.4 Parallel f-structure P.- 17.5 Sectional curvature.- 17.6 L. c. cosymplectic structures.- 17.7 Chen's class.- 17.8 Geodesic symmetries.- 17.9 Submersed CR submanifolds.- A Boothby-Wang fibrations.- B Riemannian submersions.