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Harmonic sections of Riemannian vector bundles, and metrics of Cheeger–Gromoll type by M. Benyounes; E. Loubeau; C.M. Wood is a Mathematics article available to read on EtoBox.
What is Harmonic sections of Riemannian vector bundles, and metrics of Cheeger–Gromoll type about?
We study harmonic sections of a Riemannian vector bundle E → M when E 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 E with respect to h p,q for all q. In both compact and noncompact cases, Bernstein regions of the (p, q)-plane are identified, where the only harmonic sections of E with respect to h p,q are parallel. Examples are constructed of vector fields which are harmonic sections of E = T M in the case where M is compact and has non-zero Euler characteristic.
Who reads Harmonic sections of Riemannian vector bundles, and metrics of Cheeger–Gromoll type?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- M. Benyounes; E. Loubeau; C.M. Wood
- Publisher
- Elsevier Science; Elsevier ; Elsevier BV (ISSN 0926-2245)
- Published
- 2007
- Language
- EN
- Field
- Mathematics (Physical Sciences)