A Review of Covariant Derivative Operators in Complex Vector Bundles

Abstract

In this chapter, we will briefly review covariant derivative operators in complex vector bundles. A full discussion of the contents of this chapter may be found in [21]. For the same reason as in Section 2.5, that since there is a one-to-one correspondence between covariant derivative operators and connections, a covariant derivative operator will be called a connection. We will assume that every object in hand is smooth unless otherwise stated.