Modern Geometry - Methods and Applications: Part I: The Geometry of Surfaces, Transformation Groups, and Fields (Google eBook)
Springer, 1992 - Language Arts & Disciplines - 470 pages
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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The Behaviour of Tensors Under Mappings
The Differential Calculus of Tensors
SkewSymmetric Tensors and the Theory of Integration
Differential Forms on Complex Spaces
Covariant Differentiation and the Metric
The Second Fundamental Form
The Metric on the Sphere
Spacelike Surfaces in PseudoEuclidean Space
The Language of Complex Numbers in Geometry
The Conformal Form of the Metric on a Surface
Transformation Groups as Surfaces in NDimensional Space
Conformal Transformations of Euclidean and PseudoEuclidean Spaces of Several Dimensions
Tensors The Algebraic Theory
The General Definition of a Tensor
Tensors of Type 0 k
Tensors in Riemannian and PseudoRiemannian Spaces
The Crystallographic Groups and the Finite Subgroups of the Rotation Group of Euclidean 3Space Examples of Invariant Tensors
Rank 2 Tensors in PseudoEuclidean Space and Their Eigenvalues
The Curvature Tensor
The Elements of the Calculus of Variations
The Geometrical Theory of Phase Space
The Second Variation for the Equation of the Geodesies
The Calculus of Variations in Several Dimensions Fields and Their Geometric Invariants
Examples of Lagrangians
The Simplest Concepts of the General Theory of Relativity
The Spinor Representations of the Groups SO3 and O3 1 Diracs Equation and Its Properties
Covariant Differentiation of Fields with Arbitrary Symmetry
Examples of GaugeInvariant Functionals Maxwells Equations and the YangMills Equation Functionals with Identically Zero Variational Derivative C...
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 ...
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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) ...
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da Vinci, Leonardo Leonardo da Vinci, Nature Studies from the Royal Library at Windsor Castle Royal Academy of Arts/Johnson Reprint Corp., 1981. ...
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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 ...
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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 ...
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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