Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

Conformal submersions are a natural generalisation of Riemannian submersions. Under an additional assumption of fibers being totally umbilical (which is a reasonable geometric condition, due to the conformal invariance of umbilicity), we examine those mappings, obtaining their existence conditions expressed in terms of curvatures of the domain and the image. We also present a number of examples of conformal submersions with umbilical fibers and discuss their relations with Riemannian submersions.