Twistor spaces and the general adiabatic expansions

We investigate the behavior of derivatives of the fundamental solution of a parabolic equation for the square of Dirac operator on a twistor space when the metric is blown up in the base space direction. Such a blowing up operation is expected to be an effective method for extracting some intrinsic values from various geometric invariants, most of whose cores consist of some derivatives of the fundamental solution. © 2007 Elsevier Inc. All rights reserved