Abstract
We study harmonic sections of a Riemannian vector bundle epsilon -> M when epsilon is equipped with a 2-parameter family of metrics h(p,q) which includes both the Sasaki and Cheeger-Gromoll metrics. For every k > 0 there exists a unique p such that the harmonic sections of the radius-k sphere subbundle are harmonic sections of epsilon with respect to h(p,q) for all q. In both compact and non-compact cases, Bernstein regions of the (p, q)-plane are identified, where the only harmonic sections of E with respect to hp., are parallel. Examples are constructed of vector fields which are harmonic sections of epsilon = TM in the case where M is compact and has non-zero Euler characteristic. (c) 2006 Elsevier B.V. All rights reserved.
| Original language | English |
|---|---|
| Pages (from-to) | 322-334 |
| Number of pages | 12 |
| Journal | Differential Geometry and its Applications |
| Volume | 25 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Jun 2007 |
Keywords
- (p,q)-harmonic section
- Sasaki metric
- Cheeger-Gromoll metric
- strictly q-Riemannian section
- Kato inequality
- Bernstein region
- Hopf vector field
- conformal gradient field
- FIELDS
- ENERGY
- MANIFOLDS
- CURVATURE
- MAPS