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Affine structures and holomorphic affine connections
Projective structures and holomorphic projective connections
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admits affine structure affine transformation argument assume assumption ball Bergman metric bisectional curvature bounded carries compact complex manifold condition connection constant continuous convex course covariant covering defined definition denote differential discussion distance domain equation equivalent example exhaustion function exists fact fixed frame geodesic geometry given global section harmonic Hence Hermitian metric holomorphic functions holomorphic sectional holomorphic vector bundle Kähler manifold Kähler metric Lecture locally matrix metric g natural nonnegative nonpositive normal Note parallel particular pole positive preceding problem projective proof properties prove radial curvature recall relative respect restriction Ricci satisfies sectional curvature sense simply connected solution space Stein manifold strictly plurisubharmonic structure Subsection sufficiently Suppose surface symmetric tangent tensor field Theorem transformation unit usual vanish vector fields write zero