The Resource Introduction to geometry of manifolds with symmetry, by V.V. Trofimov

Introduction to geometry of manifolds with symmetry, by V.V. Trofimov

Label
Introduction to geometry of manifolds with symmetry
Title
Introduction to geometry of manifolds with symmetry
Statement of responsibility
by V.V. Trofimov
Creator
Subject
Language
  • eng
  • rus
  • eng
Member of
Action
committed to retain for EAST
Cataloging source
DLC
http://library.link/vocab/creatorDate
1952-
http://library.link/vocab/creatorName
Trofimov, V. V.
Illustrations
illustrations
Index
index present
LC call number
QA447
LC item number
.T7613 1994
Literary form
non fiction
Nature of contents
bibliography
Series statement
Mathematics and its applications
Series volume
v. 270
http://library.link/vocab/subjectName
  • Geometry
  • Manifolds (Mathematics)
  • Symmetry
  • Geometry
  • Manifolds (Mathematics)
  • Symmetry
  • Géométrie différentielle
  • Groupe Lie
  • Algèbre Lie
  • Espace symétrique
  • Fibré vectoriel
  • Classe caractéristique
  • Classe Euler
  • Crochet Poisson
  • Geometry
  • Manifolds (Mathematics)
  • Symmetry
  • Géométrie
  • Variétés (mathématiques)
Label
Introduction to geometry of manifolds with symmetry, by V.V. Trofimov
Instantiates
Publication
Bibliography note
Includes bibliographical references (p. 321-322) and index
Carrier category
volume
Carrier category code
nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Ch. I. Elements of differential geometry. 1. The notion of a topological space. 2. Continuous mappings of topological spaces. 3. Countability axioms. 4. Quasi-compact topological spaces. 5. Separation axioms. 6. Sequentially compact topological spaces. 7. Construction of topological spaces. 8. Smooth manifolds. 9. Geometry of smooth manifolds. 10. Elements of tensor algebra. 11. Smooth mappings of smooth manifolds. 12. Exterior differential forms on manifolds. 13. Integration of exterior differential forms. 14. De Rham cohomology. 15. Elements of Riemannian geometry. 16. Elements of affine geometry. 17. Curvature tensor. 18. Geodesics and the shortest -- Ch. II. Lie Groups and Lie Algebras. 1. Lie groups. 2. Lie algebras. 3. Trajectories of left-invariant vector fields. 4. The exponential mapping. 5. Displacement of functions along trajectories. 6. Actions of Lie groups. 7. Linear representations of Lie groups. 8. Automorphisms of Lie groups. 9. Maurer-Cartan formula
  • 10. Basic global theorems about Lie groups. 11. Problems of non-simple connectedness. Coverings. 12. Lie subgroups. 13. Nilpotent representations of Lie algebras. 14. Solvable Lie algebras and their linear representations. 15. Representations of nilpotent Lie algebras. 16. Semisimple Lie algebras. 17. Cartan subalgebras. 18. Killing metric. 19. Cartan's criterion. 20. Structure of semisimple Lie algebras. 21. Simple Lie algebras. 22. Analyticity -- Ch. III. Symmetric spaces. 1. Notion of a symmetric space. 2. Compact Lie groups as Riemannian symmetric spaces. 3. Involute automorphisms of Lie groups and related Riemannian symmetric spaces. 4. Connections in principal bundles. 5. Basic theorems. 6. Lie groups as symmetric spaces. 7. Totally geodesic submanifolds. 8. Totally geodesic submanifolds and involute automorphisms. 9. Riemannian symmetric spaces -- Ch. IV. Smooth vector bundles and characteristic classes. 1. Vector bundles. 2. Connections and metrics in bundles
  • 3. Covariant derivation and curvature. 4. Characteristic classes of vector bundles. 5. Basic characteristics classes. 6. Connectedness structures in principal bundles of frames. 7. Transgression. 8. The Euler class. 9. Geometric sense of the Euler class in dimension two. 10. Geometric sense of the Euler class in higher dimensions -- Ch. V. Applications. 1. Commutation equations for differential operators. 2. Poisson brackets of hydrodynamic type and left-symmetric algebras. 3. Differential equations of motion of rigid body about a fixed point. 4. Compatible Poisson brackets. 5. Invariants of coadjoint representation
Dimensions
25 cm.
Extent
xi, 326 pages
Isbn
9780792325611
Lccn
93043036
Media category
unmediated
Media MARC source
rdamedia
Media type code
n
Other physical details
illustrations
System control number
  • (OCoLC)29428014
  • (OCoLC)ocm29428014
Label
Introduction to geometry of manifolds with symmetry, by V.V. Trofimov
Publication
Bibliography note
Includes bibliographical references (p. 321-322) and index
Carrier category
volume
Carrier category code
nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Ch. I. Elements of differential geometry. 1. The notion of a topological space. 2. Continuous mappings of topological spaces. 3. Countability axioms. 4. Quasi-compact topological spaces. 5. Separation axioms. 6. Sequentially compact topological spaces. 7. Construction of topological spaces. 8. Smooth manifolds. 9. Geometry of smooth manifolds. 10. Elements of tensor algebra. 11. Smooth mappings of smooth manifolds. 12. Exterior differential forms on manifolds. 13. Integration of exterior differential forms. 14. De Rham cohomology. 15. Elements of Riemannian geometry. 16. Elements of affine geometry. 17. Curvature tensor. 18. Geodesics and the shortest -- Ch. II. Lie Groups and Lie Algebras. 1. Lie groups. 2. Lie algebras. 3. Trajectories of left-invariant vector fields. 4. The exponential mapping. 5. Displacement of functions along trajectories. 6. Actions of Lie groups. 7. Linear representations of Lie groups. 8. Automorphisms of Lie groups. 9. Maurer-Cartan formula
  • 10. Basic global theorems about Lie groups. 11. Problems of non-simple connectedness. Coverings. 12. Lie subgroups. 13. Nilpotent representations of Lie algebras. 14. Solvable Lie algebras and their linear representations. 15. Representations of nilpotent Lie algebras. 16. Semisimple Lie algebras. 17. Cartan subalgebras. 18. Killing metric. 19. Cartan's criterion. 20. Structure of semisimple Lie algebras. 21. Simple Lie algebras. 22. Analyticity -- Ch. III. Symmetric spaces. 1. Notion of a symmetric space. 2. Compact Lie groups as Riemannian symmetric spaces. 3. Involute automorphisms of Lie groups and related Riemannian symmetric spaces. 4. Connections in principal bundles. 5. Basic theorems. 6. Lie groups as symmetric spaces. 7. Totally geodesic submanifolds. 8. Totally geodesic submanifolds and involute automorphisms. 9. Riemannian symmetric spaces -- Ch. IV. Smooth vector bundles and characteristic classes. 1. Vector bundles. 2. Connections and metrics in bundles
  • 3. Covariant derivation and curvature. 4. Characteristic classes of vector bundles. 5. Basic characteristics classes. 6. Connectedness structures in principal bundles of frames. 7. Transgression. 8. The Euler class. 9. Geometric sense of the Euler class in dimension two. 10. Geometric sense of the Euler class in higher dimensions -- Ch. V. Applications. 1. Commutation equations for differential operators. 2. Poisson brackets of hydrodynamic type and left-symmetric algebras. 3. Differential equations of motion of rigid body about a fixed point. 4. Compatible Poisson brackets. 5. Invariants of coadjoint representation
Dimensions
25 cm.
Extent
xi, 326 pages
Isbn
9780792325611
Lccn
93043036
Media category
unmediated
Media MARC source
rdamedia
Media type code
n
Other physical details
illustrations
System control number
  • (OCoLC)29428014
  • (OCoLC)ocm29428014

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