Harmonic Variables for Laplace Operators on Homogeneous Spaces

I. V. Shirokov

Harmonic Variables for Laplace Operators on Homogeneous Spaces

Differential Geometry 2026-07-09 v1

Authors: I. V. Shirokov

Abstract

A definition of harmonic variables for Laplace operators on Riemannian and pseudo-Riemannian spaces is introduced. Harmonic variables allow, in particular, the construction of particular (non-invariant group) solutions to a wide class of nonlinear differential equations. For Lie groups with a bi-invariant metric and a certain class of homogeneous spaces (e.g., symmetric spaces), an algorithm for constructing such variables is presented.

Cite

@article{arxiv.2607.14132,
  title  = {Harmonic Variables for Laplace Operators on Homogeneous Spaces},
  author = {I. V. Shirokov},
  journal= {arXiv preprint arXiv:2607.14132},
  year   = {2026}
}