Smooth Manifolds and Fibre Bundles with Applications to Theoretical Physics

Download or read book Smooth Manifolds and Fibre Bundles with Applications to Theoretical Physics written by Steinar Johannesen and published by Chapman & Hall/CRC. This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covariant derivative of forms on principal bundles -- The curvature form -- Horizontal lifts of vector fields -- Local sections and trivializations -- Horizontal lifts of curves -- Parallel transport -- Forms in associated bundles -- Covariant derivative of sections in associated vector bundles -- Covariant derivative of tensor fields -- Covariant derivative of sections along smooth maps -- Linear connections -- Koszul connections -- Structure equations -- Geodesics -- Metrical connections -- The Schwarzschild - de Sitter spacetime -- Affine transformations and Killing vector fields -- Conformal transformations -- 11 ISOMETRIC IMMERSIONS AND THE SECOND FUNDAMENTAL FORM -- Connections in reduced subbundles -- The normal bundle and the bundle of adapted orthonormal frames -- The second fundamental form -- The shape tensor -- The shape operator -- The formulae of Gauss and Weingarten -- Strain and vorticity -- The equations of Gauss, Ricci and Codazzi -- Pseudo-Riemannian hypersurfaces -- The Robertson-Walker spacetime -- The Friedmann cosmological models -- 12 JET BUNDLES -- Bundles -- Affine bundles -- Derivations and the Frölicher-Nijenhuis bracket -- First order jet bundles -- Holonomic tangent vectors -- Contact cotangent vectors -- Jet fields and connections -- Equivariant jet fields -- Second order jet bundles -- Prolongation of vector fields -- Calculus of variations -- A: PRELIMINARIES -- Maps -- The permutation group -- Group actions -- Categories and functors -- Connectivity -- Homotopy theory -- Coverings -- Topological groups -- Topological vector spaces -- Bibliography -- Index