A characterization of harmonic foliations by variations of the metric
HTML articles powered by AMS MathViewer
- by Michael D. Hvidsten and Philippe Tondeur PDF
- Proc. Amer. Math. Soc. 98 (1986), 359-362 Request permission
Abstract:
In this paper it is shown that a harmonic Riemannian foliation of a Riemannian manifold can be characterized as being a critical point of the energy of the foliation under certain variations of the manifold’s Riemannian metric. These variations are those induced by the flows of vector fields on the manifold.References
- M. Berger and D. Ebin, Some decompositions of the space of symmetric tensors on a Riemannian manifold, J. Differential Geometry 3 (1969), 379–392. MR 266084
- David G. Ebin, The manifold of Riemannian metrics, Global Analysis (Proc. Sympos. Pure Math., Vol. XV, Berkeley, Calif., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 11–40. MR 0267604
- J. Eells and L. Lemaire, A report on harmonic maps, Bull. London Math. Soc. 10 (1978), no. 1, 1–68. MR 495450, DOI 10.1112/blms/10.1.1
- James Eells Jr. and J. H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964), 109–160. MR 164306, DOI 10.2307/2373037
- Franz W. Kamber and Philippe Tondeur, Harmonic foliations, Harmonic maps (New Orleans, La., 1980) Lecture Notes in Math., vol. 949, Springer, Berlin-New York, 1982, pp. 87–121. MR 673585
- Bruce L. Reinhart, Foliated manifolds with bundle-like metrics, Ann. of Math. (2) 69 (1959), 119–132. MR 107279, DOI 10.2307/1970097
- Dennis Sullivan, A homological characterization of foliations consisting of minimal surfaces, Comment. Math. Helv. 54 (1979), no. 2, 218–223. MR 535056, DOI 10.1007/BF02566269
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 98 (1986), 359-362
- MSC: Primary 57R30; Secondary 53C12, 58D17, 58E11, 58E20
- DOI: https://doi.org/10.1090/S0002-9939-1986-0854047-4
- MathSciNet review: 854047