Transformation Groups in Differential Geometry

1-parameter group affine connection affine transformations Akad Amer automorphism group canonical form Cartan connection Chapter compact Kähler manifold complex manifold conformal structure conformal transformations coordinate system x¹ corresponding curvature defined denote diffeomorphism Differential Geometry dimension Dokl element fibre formula function G-structure geodesic GL(n graded Lie algebra h₁ Hence holomorphic holomorphic transformations holomorphic vector field induced infinitesimal automorphism infinitesimal isometry integrable invariant isometry isomorphism isotropy subgroup Kähler manifold Kobayashi Kobayashi-Nomizu Lie group Lie transformation group line bundle linear frames linear transformations mapping matrix n-dimensional Nagoya Math Nauk SSSR neighborhood nonzero obtain P¹(M Paris Sér principal bundle projective structure Proof of Lemma proof of Theorem Proposition prove pseudogroup resp Ricci tensor Riemannian manifold Riemannian metric simply connected subbundle submanifold subspace symplectic tangent space Theorem 3.1 Trans transformation group V₁ vanishes variétés Yano