A Bochner Formula for Harmonic Maps into Non-Positively Curved Metric Spaces
| Autor: | Brian Freidin |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics Applied Mathematics 010102 general mathematics Harmonic map Order (ring theory) Metric Geometry (math.MG) Curvature Space (mathematics) 01 natural sciences Domain (mathematical analysis) 010101 applied mathematics Metric space Mathematics - Metric Geometry Differential Geometry (math.DG) FOS: Mathematics Mathematics::Differential Geometry 0101 mathematics Constant (mathematics) Analysis Ricci curvature Mathematics |
| DOI: | 10.48550/arxiv.1605.08461 |
| Popis: | We study harmonic maps from Riemannian manifolds into arbitrary non-positively curved and CAT(-1) metric spaces. First we discuss the domain variation formula with special emphasis on the error terms. Expanding higher order terms of this and other formulas in terms of curvature, we prove an analogue of the Eels-Sampson Bochner formula in this more general setting. In particular, we show that harmonic maps from spaces of non-negative Ricci curvature into non-positively curved spaces have subharmonic energy density. When the domain is compact the energy density is constant, and if the domain has a point of positive Ricci curvature every harmonic map into an NPC space must be constant. Comment: 32 pages, Updated to include results on CAT(-1) targets |
| Databáze: | OpenAIRE |
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