Year: 2026
Type: preprint
Abstract: In this note, we prove that for n > 2 a harmonic map $\mathbb{S}^n \to \mathbb{CP}^m$, of index n+1 is pseudo horizontally weakly conformal, that $n$ must be odd. In particular, for even n every non-constant harmonic map $\mathbb{S}^n \to \mathbb{CP}^m$ has index at least n+2. We also present a harmonic map from $\mathbb{S}^4$ to $\mathrm{Gr}_{\mathbb{C}}(2,4)$ of index 5 that is not pseudo horizontally weakly conformal, so the statement does not extend to Grassmannians.
Source: arXiv (Cornell University)
Author: Egor, Surkov
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214747417