K. D. Elworthy (auth.), Yoshiaki Maeda, Takushiro Ochiai, Peter Michor, Akira Yoshioka (eds.)9780817645120, 0817645128, 0817645306, 9780817645304
This volume is composed of invited expository articles by well-known mathematicians in differential geometry and mathematical physics that have been arranged in celebration of Hideki Omori’s recent retirement from Tokyo University of Science and in honor of his fundamental contributions to these areas.
The papers focus on recent trends and future directions in symplectic and Poisson geometry, global analysis, infinite-dimensional Lie group theory, quantizations and noncommutative geometry, as well as applications of partial differential equations and variational methods to geometry. These articles will appeal to graduate students in mathematics and quantum mechanics, as well as researchers, differential geometers, and mathematical physicists.
Contributors include: M. Cahen, D. Elworthy, A. Fujioka, M. Goto, J. Grabowski, S. Gutt, J. Inoguchi, M. Karasev, O. Kobayashi, Y. Maeda, K. Mikami, N. Miyazaki, T. Mizutani, H. Moriyoshi, H. Omori, T. Sasai, D. Sternheimer, A. Weinstein, K. Yamaguchi, T. Yatsui, and A. Yoshioka.
Table of contents :
Front Matter….Pages i-xix
Front Matter….Pages 1-1
Aspects of Stochastic Global Analysis….Pages 3-24
A Lie Group Structure for Automorphisms of a Contact Weyl Manifold….Pages 25-44
Front Matter….Pages 45-45
Projective Structures of a Curve in a Conformal Space….Pages 47-51
Deformations of Surfaces Preserving Conformal or Similarity Invariants….Pages 53-67
Global Structures of Compact Conformally Flat Semi-Symmetric Spaces of Dimension 3 and of Non-Constant Curvature….Pages 69-83
Differential Geometry of Analytic Surfaces with Singularities….Pages 85-89
Front Matter….Pages 91-91
The Integration Problem for Complex Lie Algebroids….Pages 93-109
Reduction, Induction and Ricci Flat Symplectic Connections….Pages 111-129
Local Lie Algebra Determines Base Manifold….Pages 131-145
Lie Algebroids Associated with Deformed Schouten Bracket of 2-Vector Fields….Pages 147-160
Parabolic Geometries Associated with Differential Equations of Finite Type….Pages 161-209
Front Matter….Pages 211-211
Toward Geometric Quantum Theory….Pages 213-251
Resonance Gyrons and Quantum Geometry….Pages 253-275
A Secondary Invariant of Foliated Spaces and Type III λ von Neumann Algebras….Pages 277-286
The Geometry of Space-Time and Its Deformations from a Physical Perspective….Pages 287-301
Geometric Objects in an Approach to Quantum Geometry….Pages 303-324
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