Research Catalog

Title

The geometry of Lagrange spaces : theory and applications / by Radu Miron and Mihai Anastasiei.

Author

Miron, Radu.

Publication

Dordrecht, Netherlands ; Boston : Kluwer Academic, [1994], ©1994.

Items in the Library & Off-site

Holdings

Details

Additional Authors

Anastasiei, Mihai.

Description

xiv, 285 pages; 25 cm.

Series Statement

Fundamental theories of physics ; v. 59

Uniform Title

Fundamental theories of physics ; v. 59.

Subject

• Lagrange spaces
• Mathematical physics
• Differential geometry

Bibliography (note)

• Includes bibliographical references (p. [276]-283) and index.

Contents

• Ch. I. Fibre Bundles. General Theory. 1. Fibre Bundles. 2. Principal Fibre Bundles. 3. Vector Bundles. 4. Morphisms of Vector Bundles. 5. Vector Subbundles. 6. Operations with Vector Bundles. 7. Principal Bundle Associated with a Vector Bundle. 8. Sections in Vector Bundles -- Ch. II. Connections in Fibre Bundles. 1. Non-linear Connections in Vector Bundles. 2. Local Representations of a Non-linear Connection. 3. Other Characterisations of a Non-linear Connection. 4. Vertical and Horizontal Lifts. 5. Curvature of a Non-linear Connection. 6. Affine Morphisms of Vector Bundles -- Ch. III. Geometry of the Total Space of a Vector Bundle. 1. d-Connections on the Total Space of a Vector Bundle. 2. Local Representation of d-Connections. 3. Torsion and Curvature of d-Connections. 4. Structure Equations of a d-Connection. 5. Metric Structures on the Total Space of a Vector Bundle -- Ch. IV. Geometrical Theory of Embeddings of Vector Bundles. 1. Embeddings of Vector Bundles. 2. Moving Frame on E' in E.
• 3. Induced Non-linear Connections. Relative Covariant Derivative. 4. The Gauss-Weingarten Formulae. 5. The Gauss-Codazzi Equations -- Ch. V. Einstein Equations. 1. Einstein Equations. 2. Einstein Equations in the Case m = 1. 3. Another Form of the Einstein Equations. 4. Einstein Equations for some particular metrics on E -- Ch. VI. Generalized Einstein-Yang Mills Equations. 1. Gauge Transformations. 2. Gauge Covariant Derivatives. 3. Metrical Gauge d-Connections. 4. Generalized Einstein-Yang Mills Equations -- Ch. VII. Geometry of the Total Space of a Tangent Bundle. 1. Non-linear Connections in Tangent Bundle. 2. Semisprays, Sprays and Non-linear Connections. 3. Torsions and Curvature of a Non-linear Connections. 4. Transformations of Non-linear Connections. 5. Normal d-Connections on TM. 6. Metrical Structures on TM. 7. Some Remarkable Metrics on TM -- Ch. VIII. Finsler Spaces. 1. The Notion of Finsler Space. 2. Non-linear Cartan Connection. 3. Geodesics. 4. Metrical Cartan Connection.
• 5. Structure Equations. Bianchi Identities. 6. Remarkable Finslerian Connections. 7. Almost Kahlerian Model of a Finsler Space. 8. Subspaces in a Finsler Space -- Ch. IX. Lagrange Spaces. 1. The Notion of Lagrange Space. 2. Euler-Lagrange Equations. Canonical Non-linear Connection. 3. Canonical Metrical d-Connection. 4. Gravitational and Electromagnetic Fields. 5. Lagrange Space of Electrodynamics. 6. Almost Finslerian Lagrange Spaces. 7. Almost Kahlerian Model of a Lagrange Space -- Ch. X. Generalized Lagrange Space. 1. Notion of Generalized Lagrange Space. 2. Metrical d-Connections in a GL[superscript n] Space. 3. Structure Equations. Parallelism. 4. On h-Covariant Constant d-Tensor Fields. 5. Gravitational Field. 6. Electromagnetic Field. 7. Almost Hermitian Model of a GL[superscript n] Space -- Ch. XI. Applications of the GL[superscript n] Spaces with the Metric Tensor e[superscript 2[delta](x,y)][gamma][subscript ij](x,y).
• 1. EPS conditions and the Metric e[superscript 2[delta](x,y)][gamma][subscript ij](x,y). 2. Canonical Metrical d-Connection. 3. Electromagnetic and Gravitational Fields. 4. Two Particular Cases. 5. GL[superscript n] Spaces with the Metric e[superscript 2[delta](x,y)][gamma][subscript ij](x,y). 6. Antonelli's Metrics -- 7. General Case -- Ch. XII. Relativistic Geometrical Optics. 1. Synge Metric in Dispersive Media. 2. A Post-Newtonian Estimation. 3. A Non-linear Connection. 4. Canonical Metrical d-Connection. 5. Electromagnetic Tensors. 6. Einstein Equations. 7. Locally Minkowski GL[superscript n] Spaces. 8. Almost Hermitian Model. 9. A Finslerian Approach to the Relativistic Optics -- Ch. XIII. Geometry of Time Dependent Lagrangians. 1. Non-linear Connections in [xi] = (R x TM, [pi], R x M). 2. Time Dependent Lagrangians. 3. Non-linear Connection and Semisprays. 4. Normal d-Connections on R x TM. 5. Metrical Normal d-Connections on R x TM. 6. Rheonomic Finsler Spaces.
• 7. Remarkable Time Dependent Lagrangians. 8. Metrical Almost Contact Model of a Rheonomic Lagrange Space. 9. Generalized Rheonomic Lagrange Spaces.

ISBN

0792325915 :

LCCN

gb 94003654

OCLC

• 30399090
• ocm30399090

Owning Institutions

Columbia University Libraries