Differential Geometry of Frame Bundles

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 (02). - 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 (11)-tensor fields. - 8. 3 Application to polynomial structures on FM. - 8. 4 G-structures defined by (02)-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. Language: English