Author | Cordero, Luis A. author |
---|---|
Title | Differential Geometry of Frame Bundles [electronic resource] / by Luis A. Cordero, C. T. J. Dodson, Manuel de Leรณn |
Imprint | Dordrecht : Springer Netherlands, 1989 |
Connect to | http://dx.doi.org/10.1007/978-94-009-1265-6 |
Descript | X, 234 p. online resource |
1 The Functor Jp1 -- 1.1 The Bundle Jp1M ? M -- 1.2 Jp1G for a Lie group G -- 1.3 Jp1V for a vector space V -- 1.4 The embedding jp -- 2 Prolongation of G-structures -- 2.1 Imbedding of Jn1FM into FFM -- 2.2 Prolongation of G-structures to FM -- 2.3 Integrability -- 2.4 Applications -- 3 Vector-valued differential forms -- 3.1 General Theory -- 3.2 Applications -- 4 Prolongation of linear connections -- 4.1 Forms with values in a Lie algebra -- 4.2 Prolongation of connections -- 4.3 Complete lift of linear connections -- 4.4 Connections adapted to G-structures -- 4.5 Geodesics of ?C -- 4.6 Complete lift of derivations -- 5 Diagonal lifts -- 5.1 Diagonal lifts -- 5.2 Applications -- 6 Horizontal lifts -- 6.1 General theory -- 6.2 Applications -- 7 Lift GD of a Riemannian G to FM -- 7.1 GD, G of type (0,2) -- 7.2 Levi-Civita connection of GD -- 7.3 Curvature of GD -- 7.4 Bundle of orthonormal frames -- 7.5 Geodesics of GD -- 7.6 Applications -- 8 Constructing G-structures on FM -- 8.1 ?-associated G-structures on FM -- 8.2 Defined by (1,1)-tensor fields -- 8.3 Application to polynomial structures on FM -- 8.4 G-structures defined by (0,2)-tensor fields -- 8.5 Applications to almost complex and Hermitian structures -- 8.6 Application to spacetime structure -- 9 Systems of connections -- 9.1 Connections on a fibred manifold -- 9.2 Principal bundle connections -- 9.3 Systems of connections -- 9.4 Universal Connections -- 9.5 Applications -- 10 The Functor Jp2 -- 10.1 The Bundle Jp2M ? M -- 10.2 The second order frame bundle -- 10.3 Second order connections -- 10.4 Geodesics of second order -- 10.5 G-structures on F2M -- 10.6 Vector fields on F2M -- 10.7 Diagonal lifts of tensor fields -- 10.8 Natural prolongations of G-structures -- 10.9 Diagonal prolongation of G-structures