The homogeneous flow of a parallelizable manifold

Abstract

Motivated by the Hamilton's Ricci flow, we define the homogeneous flow of a parallelizable manifold and show the long time existence and uniqueness of its solutions on $[0,\infty ).$ Using this flow, we outline a simple proof of the Poincare Conjecture.

In the original version of this paper I incorrectly claimed that the homogeneous flow HF does not develop finite time singularities. This mistake is corrected in this version