Equivalence Between Principal Connections on the Frame Bundle and Covariant Derivatives Geometry Partition of Unity Gluing Lemma for Vector Bundle Sections Geometry Pullback of Kähler Classes under Holomorphic Maps Geometry Total Chern Class of Complex Projective Space Geometry Local Formula for the Chern Connection Geometry Finite-Dimensional Lefschetz Commutation Relations Geometry Determinant Trace Formula for Matrix Exponentials Geometry Mapping Torus Fibre Bundle Theorem Geometry Geometry Area