  The present paper is devoted to the study a global aspect of the geometry of
harmonic mappings and, in particular, infinitesimal harmonic transformations,
and represents the application of our results to the theory of Ricci solutions
and the Ricci flow. These results will be obtained using the methods of
Geometric analysis and, in particular, due to theorems of Yau, Li and Schoen on
the connections between the geometry of a complete smooth manifold and the
global behavior of its subharmonic functions.
