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1.

図書
図書
1. Transformations of manifolds and applications to differential equations
Keti Tenenblat
出版情報: Harlow : Longman, 1998  x, 209 p. ; 25 cm
シリーズ名: Pitman monographs and surveys in pure and applied mathematics ; 93
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Preface
Transformations of surfaces and applications / I：
Submanifolds of constant Sectional curvature / II：
Pseudo-spherical geodesic congruences and applications / III：
The generating equation / IV：
The generating intrinsic equation / V：
Laplace transformation in higher dimensions / VI：
References
Index
Preface
Transformations of surfaces and applications / I：
Submanifolds of constant Sectional curvature / II：
2.

図書
図書
2. Geometry, physics, and systems
Robert Hermann
出版情報: New York : M. Dekker, 1973  x, 304 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 18
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3.

図書
図書
3. Geometry of nonpositively curved manifolds (: pbk. : alk. paper)
Patrick B. Eberlein
出版情報: Chicago : University of Chicago Press, 1996  449 p. ; 24 cm
シリーズ名: Chicago lectures in mathematics
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Acknowledgments
Introduction
Notation and Preliminaries / 1：
Structure of Symmetric Spaces of Noncompact Type / 2：
Tits Geometries / 3：
Action of Isometrics on M(infinity) / 4：
A Splitting Criterion / 5：
Isometries of R" / 6：
Spaces with Euclidean Factors / 7：
Mostow Rigidity Theorem / 8：
Rigidity Theorems and Characterizations of Symmetric Spaces of Higher Rank / 9：
Fundamental Group and Geometry / 10：
References
Index of Definitions and Terminology
Index of Notation
Acknowledgments
Introduction
Notation and Preliminaries / 1：
4.

図書
図書
4. Manifolds and geometry : Pisa, 1993
edited by Paolo de Bartolomeis, Franco Tricerri, Edoardo Vesentini
出版情報: Cambridge : Cambridge University Press, 1996  viii, 321 p. ; 24 cm
シリーズ名: Symposia mathematica ; vol. 36
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List of illustrations
General editor's preface
Preface
Acknowledgements
The strangest piece of news / 1：
Early life / 2：
Professor at Pisa / 3：
The proper home for his ability / 4：
Discoveries and controversies / 5：
The condemnation of Copernicanism / 6：
Controversy and new hope / 7：
The Dialogue and Galileo's condemnation / 8：
Two new sciences / 9：
Rehabilitation / 10：
Notes
Bibliography
Index
List of illustrations
General editor's preface
Preface
5.

図書
図書
5. Geometry of manifolds
edited by K. Shiohama
出版情報: Boston ; Tokyo : Academic Press, c1989  xv, 517 p. ; 24 cm
シリーズ名: Perspectives in mathematics ; v. 8
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Dynamical Systems and Geometry
Applications of Nonstandard Analysis to Stochastic Flows and Heat Kernels on Manifolds / H. Akiyama
Hamiltonian Structure and Formal Complete Integrability of Third-Order Evolution
Equations of Not Normal Type / Y. Watanabe
The Quasi-Classical Calculation of Eigenvalues for the Bochner-Laplacian on a Line Bundle / A. Yoshioka
Geometry of Submanifolds and Tensor Geometry
The Dirichlet Problem at Infinity for Harmonic Mappings between Hadamard Manifolds / K. Akutagawa
Oriented 6-Dimensional Submanifolds in the Octonians: II / H. Hashimoto
Notes on Tricerri-Vanhecke's Decomposition of Curvature Tensors / T. Kashiwada
The Structure of the Symmetric Space with Applications / T. Nagano ; M. Sumi
On Some Compact Almost K*adahler Manifolds with Constant Holomorphic Sectional Curvature / T. Sato
On the Rigidity and Homogeneity for K*adahler Submanifolds of Complex Space Forms / Y. Taniguchi
Harmonic Non-Holomorphic Maps of 2-Tori into the 2-Sphere / M. Umehara ; K. Yamada
Lie Sphere Geometry
Wave Equation and Isoparametric Hypersurfaces / J. Kaneko
Construction of Taut Embeddings and Cecil-Ryan Conjecture / R. Miyaoka ; T. Ozawa
Lie Contact Manifolds / H. Sato ; K. Yamaguchi
On Simple Graded Lie Algebras of Finite Depth / T. Yatsui
Riemannian Geometry
On Decompositions of Riemannian Manifolds with Nonnegative Ricci Curvature / R. Ichida
p-Convex Domains in Rn / J.-i. Itoh
Geodesic Spheres and Poles / M. Maeda
Topology of Complete Open Manifolds with Non-Negative Ricci Curvature / Y. Otsu
On the Isodiametric Inequality for the 2-Sphere / T. Sakai
An Isoperimetric Problem for Infinitely Connected Complete Open Surfaces / K. Shiohama ; M. Tanaka
Positively Curved Manifolds with Restricted Diameters / T. Yamaguchi
The Ideal Boundaries of Complete Open Surfaces Admitting Total Curvature c(M) = -(infinity) / T. Shioya
On the Lengths of Stable Jacobi Fields
The Geometry of Laplace Operators
Riemannian Manifolds p-Isospectral but Not (p+1)-Isospectral / A. Ikeda
On the Holomorphicity of Pluriharmonic Maps / H. Naito
On the Instability of Minimal Submanifolds and Harmonic Maps / T. Okayasu
Yang-Mills Connections
Compactifying the Moduli Space of 1-Instantons on HPn / H. Doi ; T. Okai
Spectra of Riemannian Manifolds Without Focal Points / H. Urakawa
Based Anti-Instantons and Gravitational Instantons / M. Itoh
The 2- / Y. Kamiyama
Dynamical Systems and Geometry
Applications of Nonstandard Analysis to Stochastic Flows and Heat Kernels on Manifolds / H. Akiyama
Hamiltonian Structure and Formal Complete Integrability of Third-Order Evolution
6.

図書
図書
6. Manifolds all of whose geodesics are closed (: gw ; : us ; :pbk)
Arthur L. Besse
出版情報: Berlin ; New York : Springer-Verlag, 1978  ix, 262 p. ; 25 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 93
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7.

図書
図書
7. Differential geometry : curves - surfaces - manifolds. 3rd ed
Wolfgang Kühnel ; translated by Bruce Hunt
出版情報: Providence, R.I. : American Mathematical Society, c2015  xii, 402 p. ; 22 cm
シリーズ名: Student mathematical library ; v. 77
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8.

図書
図書
8. Synthetic geometry of manifolds
Anders Kock
出版情報: Cambridge : Cambridge University Press, 2010  xiii, 302 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 180
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目次情報: 続きを見る
Preface
Acknowledgements
Calculus and linear algebra / 1：
The number line R / 1.1：
The basic infinitesimal spaces / 1.2：
The KL axiom scheme / 1.3：
Calculus / 1.4：
Affine combinations of mutual neighbour points / 1.5：
Geometry of the neighbour relation / 2：
Manifolds / 2.1：
Framings and 1-forms / 2.2：
Affine connections / 2.3：
Affine connections from framings / 2.4：
Bundle connections / 2.5：
Geometric distributions / 2.6：
Jets and jet bundles / 2.7：
Infinitesimal simplicial and cubical complex of a manifold / 2.8：
Combinatorial differential forms / 3：
Simplicial, whisker, and cubical forms / 3.1：
Coboundary/exteripr derivative / 3.2：
Integration of forms / 3.3：
Uniqueness of observables / 3.4：
Wedge/cup product / 3.5：
Involutive-distnbutions and differential forms / 3.6：
Non-abelian theory of 1-forms / 3.7：
Differential forms with values in a vector bundle / 3.8：
Crossed modules and non-abelian 2-forms / 3.9：
The tangent bundle / 4：
Tangent vectors and vector fields / 4.1：
Addition of tangent vectors / 4.2：
The log-exp bijection / 4.3：
Tangent vectors as differential operators / 4.4：
Cotangents, and the cotangent bundle / 4.5：
The differential operator of a linear connection / 4.6：
Classical differential forms / 4.7：
Differential forms with values in TM?M / 4.8：
Lie bracket of vector fields / 4.9：
Further aspects of the tangent bundle / 4.10：
Groupoids / 5：
Connections in groupoids / 5.1：
Actions of groupoids on bundles / 5.3：
Lie derivative / 5.4：
Deplacements in groupoids / 5.5：
Principal bundles / 5.6：
Principal connections / 5.7：
Holonomy of connections / 5.8：
Lie theory; non-abelian covariant derivative / 6：
Associative algebras / 6.1：
Differential forms with values in groups / 6.2：
Differential forms with values in a group bundle / 6.3：
Bianchi identity in terms of covariant derivative / 6.4：
Semidirecl products; covariant derivative as curvature / 6.5：
The Lie algebra of G / 6.6：
Group-valued vs. Lie-algebra-valued forms / 6.7：
Left-invariant distributions / 6.8：
Examples of enveloping algebras and enveloping algebra bundles / 6.10：
Jets and differential operators / 7：
Linear differential operators and their symbols / 7.1：
Linear deplacements as differential operators / 7.2：
Bundle-theoretic differential operators / 7.3：
Sheaf-theoretic differential operators / 7.4：
Metric notions / 8：
Pseudo-Riemannian metrics / 8.1：
Geometry of symmetric affine connections / 8.2：
Laplacian (or isotropic) neighbours / 8.3：
The Laplace operator / 8.4：
Appendix
Category theory / A.1：
Models; sheaf semantics / A.2：
A simple topos model / A.3：
Microlinearity / A.4：
Linear algebra over local rings; Grassmannians / A.5：
Topology / A.6：
Polynomial maps / A.7：
The complex of singular cubes / A.8：
"Nullstellensatz" in multilinear algebra / A.9：
Bibliography
Index
Preface
Acknowledgements
Calculus and linear algebra / 1：
9.

図書
図書
9. Lectures on the geometry of manifolds. 3rd ed (: hardcover)
Liviu I Nicolaescu
出版情報: Hackensack, N.J. : World Scientific, c2021  xviii, 682 p. ; 26 cm
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