Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · dg-ga/9410005

Hermitian structures and harmonic morphisms in higher dimensional Euclidean spaces

P. Baird·J. C. Wood
View original source ↗Read source document ↗Export metadata ↓

Abstract

We construct new complex-valued harmonic morphisms from Euclidean spaces from functions which are holomorphic with respect to Hermitian structures. In particular, we give the first global examples of complex-valued harmonic morphisms from ${\bf R}^n$ for each $n>4$ which do not arise from a Kähler structure; it is known that such examples do not exist for $n \leq 4$.

Explore related subjects

dg-gamath.DG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

P. Baird, J. C. Wood. 1994-10-17. Hermitian structures and harmonic morphisms in higher dimensional Euclidean spaces. https://arxiv.org/abs/dg-ga/9410005

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2025

Long time behavior of leafwise heat flow for Riemannian foliations

For any Riemannian foliation F on a closed manifold M with an arbitrary bundle-like metric, leafwise heat flow of differential forms is proved to preserve smoothness on M at infinite time. This result and its proof have consequences about the space of bundle-like metrics on M, about the dimension of the space of leafwise harmonic forms, and mainly about the second term of the differentiable spectral sequence of F.

dg-ga↗
arXiv2018

A Simple Geometric Representative for $μ$ of a Point

For $SU(2)$ (or $SO(3)$) Donaldson theory on a 4-manifold $X$, we construct a simple geometric representative for $μ$ of a point. Let $p$ be a generic point in $X$. Then the set $\{ [A] | F_A^-(p) $ is reducible $\}$, with coefficient -1/4 and appropriate orientation, is our desired geometric representative.

dg-ga↗
arXiv2013

Moduli spaces of PU(2)-monopoles

The goal of this article was the S^1-equivariant transversality-problem and the compactification-problem for the moduli spaces of (perturbed) PU(2)-monopoles. A substantially improved version entitled "Moduli spaces of PU(2)-monopoles (revised version)" which gives simpler, clearer proofs of the transversality results, has been published on arxiv in June 99 and appeared in Asian J. Math, see Moduli spaces of PU(2)-Monopoles, Asian J. Math. Vol. 4, No. 2 (2000), 391-436.

dg-ga↗