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- Title
A CLASSIFICATION OF HORIZONTALLY HOMOTHETIC SUBMERSIONS FROM SPACE FORMS OF NONNEGATIVE CURVATURE.
- Authors
YE-LIN OU; GERARD WALSCHAP
- Abstract
In this paper, it is proved that for $n\geq 2$, any horizontally homothetic submersion $\varphi :\mathbb{R}^{n+1}\longrightarrow (N^{n}, h)$ is a Riemannian submersion up to a homothety. It is also shown that if $\varphi :\mathbb{S}^{n+1}\longrightarrow (N^{n}, h)$ is a horizontally homothetic submersion, then $n=2m$, $(N^{n}, h)$ is isometric to $\mathbb{C}P^{m}$ and, up to a homothety, $\varphi$ is a standard Hopf fibration $\mathbb{S}^{2m+1} \longrightarrow \mathbb{C}P^{m}$.
- Subjects
RIEMANNIAN submersions; RIEMANNIAN geometry; SUBMERSIONS (Mathematics); HOPF algebras; ALGEBRAIC topology
- Publication
Bulletin of the London Mathematical Society, 2006, Vol 38, Issue 3, p485
- ISSN
0024-6093
- Publication type
Article
- DOI
10.1112/S0024609306018467