Modern Geometry - Methods and Applications: Part I: The Geometry of Surfaces, Transformation Groups, and Fields (Google eBook)

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Springer, 1992 - Language Arts & Disciplines - 470 pages
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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

Preface to the First Edition
v
Geometry in Regions of a Space Basic Concepts
1
Euclidean Space
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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Page 462 - Electrodynamics of Continuous Media, Course of Theoretical Physics, Vol. 8, Pergamon Press, Oxford, UK, 1982.
Page v - YN (LD Landau Institute for Theoretical Physics, Academy of Sciences of the USSR, Moscow, USSR).
Page vi - Riemannian geometry and basic topology were not included, even by departments or faculties of mathematics, as compulsory subjects in a university-level mathematical education. The standard courses in...
Page vi - The task of designing a modernized course in geometry was begun in 1971 in the mechanics division of the Faculty of Mechanics and Mathematics of Moscow State University.
Page 2 - The chief aim of analytic (or co-ordinate) geometry is to describe geometrical figures by means of algebraic formulae referred to a Cartesian system of co-ordinates of the plane or 3-dimensional space.

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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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Modern Geometry. Methods and Applications: Part 2: The Geometry and Topology of Manifolds (Graduate Texts in Mathematics) Author: ba Dubrovin ...
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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 ...
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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, ...
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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