UID:
almahu_9949697621702882
Format:
1 online resource (265 p.)
Edition:
1st ed.
ISBN:
1-280-62897-9
,
9786610628971
,
0-08-046170-0
Series Statement:
North-Holland mathematical library, v. 68
Content:
After a brief description of the evolution of thinking on Finslerian geometry starting from Riemann, Finsler, Berwald and Elie Cartan, the book gives a clear and precise treatment of this geometry. The first three chapters develop the basic notions and methods, introduced by the author, to reach the global problems in Finslerian Geometry. The next five chapters are independent of each other, and deal with among others the geometry of generalized Einstein manifolds, the classification of Finslerian manifolds of constant sectional curvatures. They also give a treatment of isometric, affine, p
Note:
Description based upon print version of record.
,
Cover; copyright; front matter; Preface; Introduction; CONTENTS; body; Chapter I Linear Connections on a Space of Linear Elements; Regular Linear Connections; Fibre Bundles V(M) and W(M); Frames and Co-frames; Tensors and Tensor forms; Linear connections; Absolute differential in a linear connection. Regular linear connection; Exterior differential forms; Curvature and Torsion of a regular linear connection; Torsion and curvature tensors of a general linear connection; Torsion tensors; Curvature tensors; Particular case of a linear connection of directions. Conditions of reduction
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Ricci identitiesBianchi identities; Torsion and Curvature defined by a covariant derivation; Chapter II Finslerian Manifolds; Metric manifolds; Euclidean connections; The system of generators on W.; Special connections; Case of orthonormal frames and local coordinates for the class of special connections; Finslerian manifolds; Finslerian connections; Curvature tensors of the Finslerian connection; Almost Euclidean connections; Chapter III Isometries and affine vector fields on the unitary tangent fibre bundle; Local group of 1-parameter local transformations and Lie derivative
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Local invariant sectionsIntroduction of a regular linear connection; The Lie derivative of a tensor in the large sense; The Lie derivative of the coefficients of a regular linear connection; Fundamental formula; Divergence formulas; Infinitesimal isometries, the compact case; Ricci curvatures and Infinitesimal isometries; Infinitesimal affine transformations; Affine infinitesimal transformations and Covariant Derivations; The group Kz(L); Transitive algebra of affine infinitesimal transformations; The Lie Algebra L; The case of Finslerian manifolds; Case of infinitesimal isometries
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Chapter IV Geometry of generalized Einstein manifoldsComparison theorem; The Laplacian defined on the unitary tangent fibre bundle and the Finslerian curvature; Case of a manifold with constant sectional curvature; Deformation of the Finslerian metric. Generalized Einstein manifolds; Fundamental lemma, Compact case; Variations of scalar curvatures; Generalized Einstein manifolds; Second variationals of the integral I(gt); Case of a conformal infinitesimal deformation; Chapter V; Properties of compact Finslerian manifolds of non-negative curvature; Landsberg manifolds
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Finslerian manifolds with minima fibrationCase of isotropic manifolds; Calculation of (d A)2 when (M, g) is a manifold with minima fibration.; Case when (M, g) is a Landsberg manifold. The calculation of ?iAj2; Case of compact Berwald manifolds; Finslerian manifolds whose fibres are totally geodesic or minima; Compact Finslerian manifolds whose indicatrix is an Einstein manifold; The first variational of I(gt); Second variational; Chapter VI Finslerian manifolds of constant sectional curvatures; Isotropic Finslerian manifolds. Notations and recalls; Finslerian manifolds; Indicatrices
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Isotropic manifolds
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English
Additional Edition:
ISBN 0-444-52106-2
Language:
English
