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1.

図書
図書
1. Differential geometry : bundles, connections, metrics and curvature (: hbk ; : pbk)
Clifford Henry Taubes
出版情報: New York ; Oxford : Oxford University Press, 2011  xiii, 298 p. ; 24 cm
シリーズ名: Oxford graduate texts in mathematics ; 23
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2.

図書
図書
2. Complex manifolds without potential theory
S.S. Chern
出版情報: Princeton, N.J. ; Toronto ; London ; Melbourne : D. Van Nostrand, 1967  iii, 92 p. ; 20 cm
シリーズ名: Van Nostrand mathematical studies ; No. 15
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3.

図書
図書
3. Global Lorentzian geometry
John K. Beem, Paul E. Ehrlich
出版情報: New York : M. Dekker, c1981  vi, 460 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 67
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4.

図書
図書
4. Differential geometry and its applications
edited by D. Krupka and A. Švec
出版情報: Dordrecht ; Tokyo : D. Reidel , Brno : J.E. Purkyně University , Norwell, MA : Distributors for the U.S.A. and Canada, Kluwer Academic Publishers, c1987  xiii, 379 p. ; 25 cm
シリーズ名: Mathematics and its applications ; East European series
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5.

図書
図書
5. Topology and geometry for physicists (: pbk)
Charles Nash, Siddhartha Sen
出版情報: London ; Tokyo : Academic Press, 1983  x, 311 p. ; 24 cm
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目次情報: 続きを見る
Preface
Basic Notions of Topology and the Value of Topological Reasoning
Differential Geometry
Manifolds and Differential Forms
The Fundamental Group
The Homology Groups
The Higher Homotopy Groups
Cohomology and De Rham Cohomology
Fibre Bundles and Further Differential Geometry
Morse Theory
Defects, Textures, and Homotopy Theory
Yang-Mills Theories
Instantons and Monopoles
Subject Index
Preface
Basic Notions of Topology and the Value of Topological Reasoning
Differential Geometry
6.

図書
図書
6. A comprehensive introduction to differential geometry. 2nd ed (: cloth set, vols. 1-5 - v. 1 :pbk)
Michael Spivak
出版情報: Houston, Texas : Publish or Perish, Inc., c1979  5 v. ; 24 cm
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7.

図書
図書
7. Differential geometry
Tanjiro Okubo
出版情報: New York : M. Dekker, c1987  xviii, 788 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 112
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8.

図書
図書
8. Geometric inequalities (: U.S. ; : Germany)
Yu.D. Burago, V.A. Zalgaller ; translated from the Russian by A.B. Sossinsky
出版情報: Berlin ; Tokyo : Springer-Verlag, c1988  xiv, 331 p. ; 24 cm
シリーズ名: Springer series in Soviet mathematics
Die Grundlehren der mathematischen Wissenschaften ; 285
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9.

図書
図書
9. Intrinsic geometry of surfaces
A.D. Aleksandrov and V.A. Zalgaller ; [translated from the Russian by J.M. Danskin]
出版情報: Providence, R.I. : American Mathematical Society, 1967  vi, 327 p. ; 23 cm
シリーズ名: Translations of mathematical monographs ; v. 15
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10.

図書
図書
10. Symplectic techniques in physics
Victor Guillemin, Shlomo Sternberg
出版情報: Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1984  xi, 468 p. ; 24 cm
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目次情報: 続きを見る
Preface
Introduction / I：
Gaussian optics / 1：
Hamilton's method in Gaussian optics / 2：
Fermat's principle / 3：
From Gaussian optics to linear optics / 4：
Geometrical optics, Hamilton's method, and the theory of geometrical aberrations / 5：
Fermat's principle and Hamilton's principle / 6：
Interference and diffraction / 7：
Gaussian integrals / 8：
Examples in Fresnel optics / 9：
The phase factor / 10：
Fresnel's formula / 11：
Fresnel optics and quantum mechanics / 12：
Holography / 13：
Poisson brackets / 14：
The Heisenberg group and representation / 15：
The Groenwald-van Hove theorem / 16：
Other quantizations / 17：
Polarization of light / 18：
The coadjoint orbit of a semidirect product / 19：
Electromagnetism and the determination of symplectic structures / 20：
Epilogue: Why symplectic geometry?
The geometry of the moment map / II：
Normal forms / 21：
The Darboux-Weinstein theorem / 22：
Kaehler manifolds / 23：
Left-invariant forms and Lie algebra cohomology / 24：
Symplectic group actions / 25：
The moment map and some of its properties / 26：
Group actions and foliations / 27：
Collective motion / 28：
Cotangent bundles and the moment map for semidirect products / 29：
More Euler-Poisson equations / 30：
The choice of a collective Hamiltonian / 31：
Convexity properties of toral group actions / 32：
The lemma of stationary phase / 33：
Geometric quantization / 34：
Motion in a Yang-Mills field and the principle of general covariance / III：
The equations of motion of a classical particle in a Yang-Mills field / 35：
Curvature / 36：
The energy-momentum tensor and the current / 37：
The principle of general covariance / 38：
Isotropic and coisotropic embeddings / 39：
Symplectic induction / 40：
Symplectic slices and moment reconstruction / 41：
An alternative approach to the equations of motion / 42：
The moment map and kinetic theory / 43：
Complete integrability / IV：
Fibrations by tori / 44：
Collective complete integrability / 45：
Collective action variables / 46：
The Kostant-Symes lemma and some of its variants / 47：
Systems of Calogero type / 48：
Solitons and coadjoint structures / 49：
The algebra of formal pseudodifferential operators / 50：
The higher-order calculus of variations in one variable / 51：
Contractions of symplectic homogeneous spaces / V：
The Whitehead lemmas / 52：
The Hochschild-Serre spectral sequence / 53：
Galilean and Poincare elementary particles / 54：
Coppersmith's theory / 55：
References
Index
Preface
Introduction / I：
Gaussian optics / 1：
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