Journal of Differential Geometry, Volume 2

a₁ abelian assume automorphism B₁ Berkeley bundle CALIFORNIA LIBRARY Cartan Chern closed ideals complex structure condition conformal transformation constant coordinate Corollary critical points curve defined denote diffeomorphism differential geometry dimension ds² e₁ element equation Euclidean space exists finite index follows function G-invariant G₁ Gauss map geodesic hence hermitian metric holomorphic imbedding immersion implies integral invariant almost complex isometric isomorphic isotropy K₁ Killing vector field Lemma Lie algebra Lie group linear linearly compact M₁ mapping Math matrix mean curvature morphism neighborhood nilpotent normal orthogonal orthonormal P₁ proof of Theorem Proposition prove pseudogroup respect Riemannian manifold riemannian metric satisfies sectional curvature semisimple simple simply connected solvable solvable group sphere subalgebra subgroup submanifold subspace Suppose symmetric spaces tensor field topological torus UNIVERSITY OF CALIFORNIA v₁ vector space w₁ X₁ y₁ zero α₁