Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The index of harmonic foliations on spheres


Authors: Franz W. Kamber and Philippe Tondeur
Journal: Trans. Amer. Math. Soc. 275 (1983), 257-263
MSC: Primary 57R30; Secondary 58E20
DOI: https://doi.org/10.1090/S0002-9947-1983-0678348-X
MathSciNet review: 678348
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For foliations on a compact oriented manifold there is a natural energy functional, defined with respect to a Riemannian metric. Harmonic Riemannian foliations are then the critical foliations for this functional under an appropriate class of special variations. The index of the title is the index of the Hessian of the energy functional at a critical, i.e., harmonic foliation. It is a finite number. In this note it is shown that for a harmonic Riemannian foliation $ \mathcal{F}$ of codimension $ q$ on the $ n$-sphere ($ n > 2$) this index is greater or equal to $ q + 1$. Thus $ \mathcal{F}$ is unstable. Moreover the given bound is best possible.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57R30, 58E20

Retrieve articles in all journals with MSC: 57R30, 58E20


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1983-0678348-X
Keywords: Harmonic foliation, index
Article copyright: © Copyright 1983 American Mathematical Society