## Geometry of Groups of Transformations |

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admits affine transformation analytic infinitesimal transformation arbitrary associated assume automorphism belongs called closed coincides compact complex components CONDITION conformal consequently constant contained corresponding covariant derivative curvature decomposition deduces defined definite denote differentiable effective element Euclidian exists fact follows formula frames G-invariant Given group G hence Hermitian holonomy group homogeneous space Vm ideal identity infinitesimal isometry invariant irreducible isomorphism Kählerian manifold Killing leaves Lemma let us consider Let us suppose Lie algebra linear connection locally manifold Vm mapping metric naturally necessarily necessary and sufficient neighbourhood obtains operator particular path positive preceding projection reductive homogeneous space relation representation respect restricted Ricci Riemannian homogeneous space Riemannian manifold satisfies scalar semi-simple simply connected solution structure subgroup subspace symmetric tangent tensor THEOREM tion transitive transport values vector field vector space yields zero