Local Normal Form for Holomorphic Immersions Geometry Associated Bundle from Cocycle Transition Data Geometry Cocycle Identities for Fibre Bundle Transition Functions Geometry Newlander Nirenberg Theorem Geometry Orthonormal Frame Reduction Geometry Clutching Classification Theorem for Vector Bundles over Spheres Geometry Smooth Fibre Bundle Structure from Compatible Local Trivializations Geometry Gauge Transformation Law for Local Curvature Forms Geometry Geometry Area