Harmonic morphisms from homogeneous Hadamard manifolds
Sigmundur Gudmundsson, Jonas Nordstr\"om
TL;DR
This paper introduces novel methods to construct complex-valued harmonic morphisms from homogeneous Hadamard manifolds and Lie groups, expanding the toolkit for geometric analysis and harmonic map theory.
Contribution
It presents new techniques for creating harmonic morphisms from Riemannian Lie groups and homogeneous Hadamard manifolds, including invariant foliations.
Findings
New solutions for harmonic morphisms from homogeneous Hadamard manifolds
A method for constructing left-invariant foliations on Lie groups
Enhanced understanding of harmonic morphism structures in Lie group settings
Abstract
We present a new method for manufacturing complex-valued harmonic morphisms from a wide class of Riemannian Lie groups. This yields new solutions from an important family of homogeneous Hadamard manifolds. We also give a new method for constructing left-invariant foliations on a large class of Lie groups producing harmonic morphisms
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometric and Algebraic Topology · Geometry and complex manifolds