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

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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 of codimension on the -sphere () this index is greater or equal to . Thus is unstable. Moreover the given bound is best possible.

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DOI:
https://doi.org/10.1090/S0002-9947-1983-0678348-X

Keywords:
Harmonic foliation,
index

Article copyright:
© Copyright 1983
American Mathematical Society