Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4606695 | Differential Geometry and its Applications | 2007 | 13 Pages |
Abstract
We study harmonic sections of a Riemannian vector bundle E→ME→M when EE is equipped with a 2-parameter family of metrics hp,qhp,q which includes both the Sasaki and Cheeger–Gromoll metrics. For every k>0k>0 there exists a unique p such that the harmonic sections of the radius-k sphere subbundle are harmonic sections of EE with respect to hp,qhp,q for all q . In both compact and non-compact cases, Bernstein regions of the (p,q)(p,q)-plane are identified, where the only harmonic sections of EE with respect to hp,qhp,q are parallel. Examples are constructed of vector fields which are harmonic sections of E=TME=TM in the case where M is compact and has non-zero Euler characteristic.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
M. Benyounes, E. Loubeau, C.M. Wood,