Real and Complex Geometry
Description
The book covers a wide area of hot subjects in real and complex differential geometry, such as conformal geometry, special holonomy, Sasakian geometry, Kähler and non-Kähler metrics, classification of compact complex surfaces, Einstein metrics, bi-Hermitian geometry, non-integrable almost complex structures, etc. All of these are rather close to Paul Gauduchon's themes and influential results in the past fifty years. The reader will find fifteen papers - a few surveys, but the majority containing new and exciting results. The book thus gives an idea of the present research interests of some of the best experts today in real and complex differential geometry including Vestislav Apostolov, Florin Belgun, Charles Boyer, Georges Dloussky, Anna Fino, Gueo Grantcharov, Claude LeBrun, Andrei Moroianu, Massimiliano Pontecorvo, Simon Salamon, Andrew Swann, Adriano Tomassini, Valentino Tosatti, and Misha Verbitsky.
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Person
Liviu Ornea (born 1960) is a professor in the Department of Mathematics at the University of Bucharest and a senior researcher at the Institute of Mathematics "Simion Stoilow" in the Romanian Academy. His main fields of interest include differential geometry of complex manifolds, with a special focus on locally conformally Kähler manifolds. He is the (co)author of more than 90 published papers and two research monographs. He has visited MPIM Bonn, ICTP Trieste, IMPA (Rio de Janeiro), Ecole Polytechnique (Palaiseau), Ecole Polytechnique Fédérale de Lausanne, Tokyo Metropolitan University, Tokyo Institute for Technology, University of New Mexico (Albuquerque), Università di Firenze, Università di Roma "La Sapienza", etc.
Content
Chapter 1. From Kähler Ricci Solitons to Calabi-Yau Kähler Cones.- Chapter 2. Projective Structures on Curves and Conformal Geometry.- Chapter 3. Constant Scalar Curvature Sasaki Metrics.- Chapter 4. A Mapping Tori Construction of Strong HKT and Generalized Hyperkähler Manifolds.- Chapter 5. Classification of Odd Generalized Einstein Metrics on 3-Dimensional Non-Unimodular Lie Groups.- Chapter 6. Cohomological Lifting of Multi-Toric Graphs.- Chapter 7. On Classification of Compact Complex Surfaces of Class VII.- Chapter 8. Conformal Vector Fields on LCP Manifolds.- Chapter 9. On Some Properties of Hopf Manifolds.- Chapter 10. Einstein Constants and Smooth Topology.- Chapter 11. The Lee-Gauduchon cone on complex manifolds.- Chapter 12. Bi-Hermitian and locally conformally Kähler surfaces.- Chapter 13. Revisiting 3-Sasakian and G2-structures.- Chapter 14. Kodaira Dimension of SU( m )-Structures.-Chapter 15. A Cheng-Yau Type Estimate for the Symplectic Calabi-Yau Equation.