<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In this paper, in the special setting of a Riemannian foliation en- dowed with a bundle-like metric, we obtain conditions that force the vanishing of the kernel of the basic Dirac operator associated to the metric; this way we extend the traditional setting of Riemannian foli- ations with basic-harmonic mean curvature, where Bochner technique and vanishing results are known to work. Beside classical conditions concerning the positivity of some curvature terms we obtain new rela- tions between the mean curvature form and the kernel of the basic Dirac operator</p></abstract>

In this paper, in the special setting of a Riemannian foliation en- dowed with a bundle-like metric, we obtain conditions that force the vanishing of the kernel of the basic Dirac operator associated to the metric; this way we extend the traditional setting of Riemannian foli- ations with basic-harmonic mean curvature, where Bochner technique and vanishing results are known to work. Beside classical conditions concerning the positivity of some curvature terms we obtain new rela- tions between the mean curvature form and the kernel of the basic Dirac operator

Riemannian foliations and the kernel of the basic Dirac operator

Department of Mathematics, University of Craiova, 13 Al.I. Cuza, Craiova, RO-200585, Romania

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

{"article-title":"Riemannian foliations and the kernel of the basic Dirac operator"}

In this paper, in the special setting of a Riemannian foliation en- dowed with a bundle-like metric, we obtain conditions that force the vanishing of the...

Riemannian foliations and the kernel of the basic Dirac operator

Published Online: May 17, 2013

Page range: 145 - 158

DOI: https://doi.org/10.2478/v10309-012-0046-z

Keywords
Riemannian foliations, Dirac bundles, vanishing results

This content is open access.

Riemannian foliations and the kernel of the basic Dirac operator

Published Online: May 17, 2013

Page range: 145 - 158

DOI: https://doi.org/10.2478/v10309-012-0046-z

KeywordsRiemannian foliations, Dirac bundles, vanishing results

This content is open access.

Keywords
Riemannian foliations, Dirac bundles, vanishing results