## Invariant connections in principal fiber bundles over locally homogeneous spaces |

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a e G a e Gu associated fiber bundle axQSi b e Gu bundle of frames canonical connection function canonical linear connection closed curve conclude connected locally homogeneous connection form cp^u definition determined diffeomorphism differentiable manifold dim.M e e G e e Gu exists a canonical exists a unique exists an invariant given decomposition gu h e H holonomy group horizontal subspace invariant connection function irE(x isomorphism isotropy group lasso Lemma 11 Lie algebra gu Lie group Lie subgroup locally homogeneous space nection neighborhood of e e one-one open bundle open sets parallel displacement principal fiber bundle proof prove reductive respect right invariant simply connected locally small representation space and E(M,S Suppose there exists tangent bundle tangent space tion u u u unique continuation variant connection vector field