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Automorphisms of GStructures
Isometries of Riemannian Manifolds
Automorphisms of Complex Manifolds
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1-parameter acting affine connection affine transformations Amer assume automorphism basis belongs called Cartan Chapter closed compact complex complex manifold components conformal connection consider consisting constant contains coordinate system corresponding curvature defined definition denote diffeomorphism dimension element equations equivalent Example exists fact finite fixed follows formula frames function G-structure geodesic Geometry given hand Hence holomorphic vector field homogeneous identity implies induced infinitesimal isometry integrable invariant isomorphism Kähler manifold Kobayashi leaves Lemma Lie algebra Lie group mapping Math matrix metric natural negative neighborhood nonzero normal obtain orientable origin parallel positive projective Proof Proof of Lemma proof of Theorem Proposition prove rank resp respect restriction result Riemannian manifold space structure subgroup submanifold symmetric symplectic tangent tensor Theorem Theorem 2.1 trans transformation group transitive unique vanishes write zero