From Geometry to Quantum Mechanics

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, M. Goto, J. Grabowski, S. Gutt, A. Inoue, S. Kaneyuki, M. Karasev, O. Kobayashi, Y. Maeda, G. Marmo, Y. Matsuyama, P.W. Michor, K. Mikami, N. Miyazaki, T. Mizutani, T. Morimoto, H. Moriyoshi, T. Nagano, Y. Nakanishi, M. Obata, H. Omori, T. Ratiu, T. Sasai, D. Sternheimer, A. Weinstein, K. Yamaguchi, and A. Yoshioka.

Preface	p. ix
Curriculum Vitae	p. xiii
Global Analysis and Infinite-Dimensional Lie Groups	p. 1
Aspects of Stochastic Global Analysis	p. 3
A Lie Group Structure for Automorphisms of a Contact Weyl Manifold	p. 25
Riemannian Geometry	p. 45
Projective Structures of a Curve in a Conformal Space	p. 47
Deformations of Surfaces Preserving Conformal or Similarity Invariants	p. 53
Global Structures of Compact Conformally Flat Semi-Symmetric Spaces of Dimension 3 and of Non-Constant Curvature	p. 69
Differential Geometry of Analytic Surfaces with Singularities	p. 85
Symplectic Geometry and Poisson Geometry	p. 91
The Integration Problem for Complex Lie Algebroids	p. 93
Reduction, Induction and Ricci Flat Symplectic Connections	p. 111
Local Lie Algebra Determines Base Manifold	p. 131
Lie Algebroids Associated with Deformed Schouten Bracket of 2-Vector Fields	p. 147
Parabolic Geometries Associated with Differential Equations of Finite Type	p. 161
Quantizations and Noncommutative Geometry	p. 211
Toward Geometric Quantum Theory	p. 213
Resonance Gyrons and Quantum Geometry	p. 253
A Secondary Invariant of Foliated Spaces and Type III[kappa] von Neumann Algebras	p. 277
The Geometry of Space-Time and Its Deformations: A Physical Perspective	p. 287
Geometric Objects in an Approach to Quantum Geometry	p. 303
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From Geometry to Quantum Mechanics

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