Topological restrictions for circle actions and harmonic morphisms
| dc.creator | Pantilie, Radu | |
| dc.creator | Wood, John C. | |
| dc.date | 2000-07-24 | |
| dc.date | 2000-10-19 | |
| dc.date.accessioned | 2026-07-07T04:36:28Z | |
| dc.date.available | 2026-07-07T04:36:28Z | |
| dc.description | Let $M^m$ be a compact oriented smooth manifold which admits a smooth circle action with isolated fixed points which are isolated as singularities as well. Then all the Pontryagin numbers of $M^m$ are zero and its Euler number is nonnegative and even. In particular, $M^m$ has signature zero. Since a non-constant harmonic morphism with one-dimensional fibres gives rise to a circle action we have the following applications: (i) many compact manifolds, for example $CP^{n}$, $K3$ surfaces, $S^{2n}\times P_g$ ($n\geq2$) where $P_g$ is the closed surface of genus $g\geq2$ can never be the domain of a non-constant harmonic morphism with one-dimensional fibres whatever metrics we put on them; (ii) let $(M^4,g)$ be a compact orientable four-manifold and $ϕ:(M^4,g)\to(N^3,h)$ a non-constant harmonic morphism. Suppose that one of the following assertions holds: (1) $(M^4,g)$ is half-conformally flat and its scalar curvature is zero, (2) $(M^4,g)$ is Einstein and half-conformally flat, (3) $(M^4,g,J)$ is Hermitian-Einstein. Then, up to homotheties and Riemannian coverings, $ϕ$ is the canonical projection $T^4\to T^3$ between flat tori. | |
| dc.description | 18 pages; Minor corrections to Proposition 3.1 and small changes in Theorem 2.8, proof of Theorem 3.3 and Remark 3.4 | |
| dc.identifier | https://arxiv.org/abs/math/0007140 | |
| dc.identifier | http://arxiv.org/abs/math/0007140 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59609 | |
| dc.subject | Differential Geometry | |
| dc.subject | Geometric Topology | |
| dc.subject | 58E20;53C43;57R20 | |
| dc.title | Topological restrictions for circle actions and harmonic morphisms | |
| dc.type | text |