## Modern Geometry - Methods and Applications: Part I: The Geometry of Surfaces, Transformation Groups, and Fields (Google eBook)This is the first volume of a three-volume introduction to modern geometry which emphasizes applications to other areas of mathematics and theoretical physics. Topics covered include tensors and their differential calculus, the calculus of variations in one and several dimensions, and geometric field theory. This new edition offers substantial revisions, and the material is written in concrete language with terminology acceptable to physicists. |

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### Contents

v | |

1 | |

9 | |

Riemannian and PseudoRiemannian Spaces | 17 |

The Simplest Groups of Transformations of Euclidean Space | 23 |

The SerretFrenet Formulae | 38 |

PseudoEuclidean Spaces | 50 |

The Theory of Surfaces | 61 |

The Behaviour of Tensors Under Mappings | 205 |

Vector Fields | 208 |

Lie Algebras | 216 |

The Differential Calculus of Tensors | 238 |

SkewSymmetric Tensors and the Theory of Integration | 248 |

Differential Forms on Complex Spaces | 270 |

Covariant Differentiation | 275 |

Covariant Differentiation and the Metric | 288 |

The Second Fundamental Form | 76 |

The Metric on the Sphere | 86 |

Spacelike Surfaces in PseudoEuclidean Space | 90 |

The Language of Complex Numbers in Geometry | 95 |

Analytic Functions | 100 |

The Conformal Form of the Metric on a Surface | 109 |

Transformation Groups as Surfaces in NDimensional Space | 120 |

Conformal Transformations of Euclidean and PseudoEuclidean Spaces of Several Dimensions | 136 |

Tensors The Algebraic Theory | 145 |

The General Definition of a Tensor | 151 |

Tensors of Type 0 k | 161 |

Tensors in Riemannian and PseudoRiemannian Spaces | 170 |

The Crystallographic Groups and the Finite Subgroups of the Rotation Group of Euclidean 3Space Examples of Invariant Tensors | 176 |

Rank 2 Tensors in PseudoEuclidean Space and Their Eigenvalues | 197 |

The Curvature Tensor | 299 |

The Elements of the Calculus of Variations | 317 |

Conservation Laws | 324 |

Hamiltonian Formalism | 337 |

The Geometrical Theory of Phase Space | 348 |

Lagrange Surfaces | 362 |

The Second Variation for the Equation of the Geodesies | 371 |

The Calculus of Variations in Several Dimensions Fields and Their Geometric Invariants | 379 |

Examples of Lagrangians | 413 |

The Simplest Concepts of the General Theory of Relativity | 416 |

The Spinor Representations of the Groups SO3 and O3 1 Diracs Equation and Its Properties | 431 |

Covariant Differentiation of Fields with Arbitrary Symmetry | 443 |

Examples of GaugeInvariant Functionals Maxwells Equations and the YangMills Equation Functionals with Identically Zero Variational Derivative C... | 453 |

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Modern geometry — methods and applications. Part II, The geometry **...**

Modern geometry—methods and applications. Part II, The geometry and. topology of manifolds, by ba Dubrovin, at Fomenko, and sp ...

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List of recommended books for Ph229: Advanced Mathematical Methods **...**

ba Dubrovin, at Fomenko, sp Novikov, "Modern Geometry - Methods and Applications," Parts 1 and 2, Springer-Verlag (1984/85). An accessible introduction to ...

www.theory.caltech.edu/ ~kapustin/ Ph229/ recbooks.html

MATH-4210, MATHEMATICAL ANALYSIS II

ba Dubrovin, at Fomenko, and sp Novikov, Modern Geometry - Methods and Applications : Part I: The Geometry of Surfaces, Transformation Groups, and Fields, ...

www.rpi.edu/ ~kovacg/ classes/ analysis2/ 421.html

Modern Geometry - Methods and Applications: Part I: The Geometry **...**

下载Free ebook:Modern Geometry - Methods and Applications: Part I: The Geometry of Surfaces, Transformation Groups, - 免费下载chm, pdf 电子书，rapidshare等 ...

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Sergei Petrovich Novikov

Uspekhi Mat. Nauk 43:4 (1988), 3-9. Russian Math. Surveys 43:4 (1988), 1-10. Sergei Petrovich Novikov. (on his fiftieth birthday) ...

www.iop.org/ EJ/ article/ 0036-0279/ 43/ 4/ M01/ RMS_43_4_M01.pdf

Stephen Wolfram: A New Kind of Science -- Relevant Books

da Vinci, Leonardo Leonardo da Vinci, Nature Studies from the Royal Library at Windsor Castle Royal Academy of Arts/Johnson Reprint Corp., 1981. ...

www.wolframscience.com/ reference/ books/ d.html

Fairbanks: Lax equation representation of certain completely **...**

5 ba Dubrovin , at Fomenko and sp Novikov : Modern Geometry - Methods and Applications, Part II, Springer-Verlag , New York , Berlin , Heidelberg , Tokyo ...

www.numdam.org/ numdam-bin/ fitem?id=CM_1988__68_1_31_0

Book List of IWAI Lab. -1986 (Author from D )

Modern Geometry - Methods and Applications. Part3. Introduction to Homol Graduate Texts in Mathematics. 124 Springer-Verlag 414.7 91089845 ...

yang.amp.i.kyoto-u.ac.jp/ research/ booklist/ D.html

Phys. Rev. B 64, 212203 (2001): Milovanov and Rasmussen - Critical **...**

A. Dubrovin, sp Novikov, and at Fomenko, Modern Geometry. Methods and Applications ~Nauka, Moscow, 1986!. 16S. Havlin and D. ben-Avraham, Adv. Phys. ...

link.aps.org/ doi/ 10.1103/ PhysRevB.64.212203