Lenticular Algebro-geometric Continuous Point-Motion (or Geodetic Line): On the Ricci & Kähler–Ricci Flow Over Time

The purpose of this article is to investigate the Ricci flow and its Kählerian version. We would like to underline the aspect that we could call lenticular of this geometric object (consisting of a specific partial differential equation), the possibility of modifying the shapes of space through it; also, an hint to the optimality of such a flow, viz. the specificity of being described in terms of optimal transport. The Kähler–Ricci flow as a parabolic complex Monge–Ampère formula is then defined, followed by a theorem on the geometric curvature evolution. In closing, there is a supporting appendix