Geometrically formal 4-manifolds with nonnegative sectional curvature
- A Riemannian manifold is called geometrically formal if the wedge product of any two harmonic forms is again harmonic. We classify geometrically formal compact 4-manifolds with nonnegative sectional curvature. If the sectional curvature is strictly positive, the manifold must be homeomorphic to S-4 or diffeomorphic to CP2. This conclusion stills holds true if the sectional curvature is strictly positive and we relax the condition of geometric formality to the requirement that the length of harmonic 2-forms is not too nonconstant. In particular, the Hopf conjecture on S-2 x S-2 holds in this class of manifolds.
| Author details: | Christian BärORCiDGND |
|---|---|
| ISSN: | 1019-8385 |
| ISSN: | 1944-9992 |
| Title of parent work (English): | Communications in analysis and geometry |
| Publisher: | International Press of Boston |
| Place of publishing: | Somerville |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2015 |
| Publication year: | 2015 |
| Release date: | 2017/03/27 |
| Volume: | 23 |
| Issue: | 3 |
| Number of pages: | 19 |
| First page: | 479 |
| Last Page: | 497 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| Peer review: | Referiert |
