Affiliation:
1. Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Abstract
For Riemannian manifoldsMandN, admitting a submersionϕwith compact fibres, we introduce the projection of a function via its decomposition into horizontal and vertical components. By comparing the Laplacians onMandN, we determine conditions under which a harmonic function onU=ϕ−1(V)⊂Mprojects down, via its horizontal component, to a harmonic function onV⊂N.
Funder
King Fahd University of Petroleum and Minerals, Dhahran
Subject
Applied Mathematics,Analysis