Horizontal Gradient Flows on the Heisenberg Group

Abstract

This paper studies horizontal gradient flows on the Heisenberg group, an important example of a sub-Riemannian manifold. The analysis focuses on horizontal differential operators and their role in describing evolution processes governed by the intrinsic geometry of the group. The work highlights the structure of the horizontal gradient and related operators, providing insight into gradient-driven dynamics and partial differential equations in non-commutative geometric settings.