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arXiv · 2607.14132

Harmonic Variables for Laplace Operators on Homogeneous Spaces

I. V. Shirokov
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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.

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I. V. Shirokov. 2026-07-09. Harmonic Variables for Laplace Operators on Homogeneous Spaces. https://arxiv.org/abs/2607.14132

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