Foundations of Differential Geometry, Volume 1 |
Contents
VI2 | 28 |
Theory of Connections | 51 |
Connections in a principal fibre bundle | 68 |
Copyright | |
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Foundations of Differential Geometry, Volume 1 Shoshichi Kobayashi,Katsumi Nomizu Limited preview - 1996 |
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1-parameter group a₁ affine connection affine mapping affine transformation analytic automorphism canonical Chapter compact components connection form constant curvature Corollary covariant curvature form curvature tensor curve defined denote diffeomorphism differentiable element Euclidean exists fibre bundle follows function geodesic given GL(n group G Hence holonomy group horizontal subspace identity implies induced infinitesimal affine transformation infinitesimal isometry invariant isometry Let f Let G Lie algebra Lie group linear connection linear holonomy group mapping f Math metric g neighborhood normal coordinate system obtain parallel displacement principal fibre bundle Proof of Lemma proof of Theorem Proposition 3.1 prove q₁ resp respect Riemannian connection Riemannian manifold Riemannian metric simply connected SO(n structure equation subgroup of G subset t₁ T₂(M tangent space tensor field Theorem 4.2 torsion u₁ unique V₁ vector field W₁ x₁ Σκ