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This volume contains research and survey articles by well known and respected mathematicians on differential geometry and topology that have been collected and dedicated in honor of Lieven Vanhecke, as a tribute to his many fruitful and inspiring contributions to these fields.
The papers, all written with the necessary introductory and contextual material, describe recent developments and research trends in spectral geometry, the theory of geodesics and curvature, contact and symplectic geometry, complex geometry, algebraic topology, homogeneous and symmetric spaces, and various applications of partial differential equations and differential systems to geometry. One of the key strengths of these articles is their appeal to non-specialists, as well as researchers and differential geometers.
Contributors: D.E. Blair; E. Boeckx; A.A. Borisenko; G. Calvaruso; V. Cortés; P. de Bartolomeis; J.C. Díaz-Ramos; M. Djoric; C. Dunn; M. Fernández; A. Fujiki; E. García-Río; P.B. Gilkey; O. Gil-Medrano; L. Hervella; O. Kowalski; V. Muñoz; M. Pontecorvo; A.M. Naveira; T. Oguro; L. Schäfer; K. Sekigawa; C-L. Terng; K. Tsukada; Z. Vlásek; E. Wang; and J.A. Wolf.
List of contents
Curvature of Contact Metric Manifolds.- A Case for Curvature: the Unit Tangent Bundle.- Convex Hypersurfaces in Hadamard Manifolds.- Contact Metric Geometry of the Unit Tangent Sphere Bundle.- Topological-antitopological Fusion Equations, Pluriharmonic Maps and Special Kähler Manifolds.- ?2 and ?-Deformation Theory for Holomorphic and Symplectic Manifolds.- Commutative Condition on the Second Fundamental Form of CR-submanifolds of Maximal CR-dimension of a Kähler Manifold.- The Geography of Non-Formal Manifolds.- Total Scalar Curvatures of Geodesic Spheres and of Boundaries of Geodesic Disks.- Curvature Homogeneous Pseudo-Riemannian Manifolds which are not Locally Homogeneous.- On Hermitian Geometry of Complex Surfaces.- Unit Vector Fields that are Critical Points of the Volume and of the Energy: Characterization and Examples.- On 3D-Riemannian Manifolds with Prescribed Ricci Eigenvalues.- Two Problems in Real and Complex Integral Geometry.- Notes on the Goldberg Conjecture in Dimension Four.- Curved Flats, Exterior Differential Systems, and Conservation Laws.- Symmetric Submanifolds of Riemannian Symmetric Spaces and Symmetric R-spaces.- Complex Forms of Quaternionic Symmetric Spaces.
Summary
* Contains research and survey articles by well known and respected mathematicians on recent developments and research trends in differential geometry and topology
* Dedicated in honor of Lieven Vanhecke, as a tribute to his many fruitful and inspiring contributions to these fields
* Papers include all necessary introductory and contextual material to appeal to non-specialists, as well as researchers and differential geometers
