Author: Ражабов, Элдор Одилбекович; Нурбоева, Махлиё Бахтиёровна; Исломов, Лазизбек Тулкин угли

Annotation: This paper investigates the geometry of orbits generated by certain families of vector fields on Riemannian manifolds. In particular, attention is given to conformal vector fields, which are defined as vector fields for which the Lie derivative of the metric tensor is proportional to the tensor itself. It is shown that families of such vector fields give rise to singular foliations, the leaves of which are smooth surfaces of zero curvature.

Keywords: Riemannian manifold, conformal vector fields, orbit, singular foliation, invariant functions, Lie derivative, one-parameter group, conformal transformations, zero curvature.

Pages in journal: 250 - 255