An optimal Loewner-type systolic inequality and harmonic one-forms of constant norm
| dc.creator | Bangert, Victor | |
| dc.creator | Katz, Mikhail | |
| dc.date | 2003-04-30 | |
| dc.date.accessioned | 2026-07-07T04:57:37Z | |
| dc.date.available | 2026-07-07T04:57:37Z | |
| dc.description | We present a new optimal systolic inequality for a closed Riemannian manifold X, which generalizes a number of earlier inequalities, including that of C. Loewner. We characterize the boundary case of equality in terms of the geometry of the Abel-Jacobi map, A_X, of X. For an extremal metric, the map A_X turns out to be a Riemannian submersion with minimal fibers, onto a flat torus. We characterize the base of J_X in terms of an extremal problem for Euclidean lattices, studied by A.-M. Bergé and J. Martinet. Given a closed manifold X that admits a submersion F to its Jacobi torus T^{b_1(X)}, we construct all metrics on X that realize equality in our inequality. While one can choose arbitrary metrics of fixed volume on the fibers of F, the horizontal space is chosen using a multi-parameter version of J. Moser's method of constructing volume-preserving flows. | |
| dc.description | 27 pages | |
| dc.identifier | https://arxiv.org/abs/math/0304494 | |
| dc.identifier | http://arxiv.org/abs/math/0304494 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67319 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C23;57N65;52C07 | |
| dc.title | An optimal Loewner-type systolic inequality and harmonic one-forms of constant norm | |
| dc.type | text |