Abstract
The purpose of this chapter is to construct exotic hypoelliptic superconnection forms associated with a holomorphic Hermitian vector bundle. This chapter prepares for Chapter 11, in which a Riemann-Roch-Grothendieck formula in Bott- Chern cohomology will be established using exotic hypoelliptic superconnections. This chapter is also related to Chapter 8, in which ordinary hypoelliptic superconnections for vector bundles were considered.
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