Summary
In this paper we study infinitesimal automorphisms of finiteL 2-norm for harmonic Riemannian and Kähler foliations admitting a complete bundle-like metric. The results generalize facts established recently in the compact case.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
T. Aoki and S. Yorozu,L 2-transverse conformal and Killing fields on complete foliated Riemannian manifolds, preprints.
A. Andreotti and E. Vesentini, Carleman estimates for the Laplace-Beltrami equation on complex manifolds, Publ. Math. IHES 25 (1965), 313–362.
S. Bochner, Vector fields and Ricci curvature, Bull. Amer. Math. Soc.52 (1946), 776–797.
J. Dodziuk, Vanishing theorems of square intergrable harmonic forms, Geometry and Analysis, Papers dedicated to the memory of V. K. Patodi (1981), 21–27.
F. W. Kamber and Ph. Tondeur, Harmonic Foliations, Proc. NSF Conference on Harmonic m maps, Tulane University (1980), Springer Lecture Notes949 (1982), 87–121.
F. W. Kamber and Ph Tondeur, Infinitesimal automorphisms and second variation of the energy for harmonic foliations, Tôhoku Math. J.34 (1982), 525–538.
F. W. Kamber and Ph Tondeur, Foliations and metrics, Proc. of the 1981–82 year in Differential Geometry, University of Maryland, Birkhäuser, Progress in Mathematics Vol.32 (1983), 103–152.
F. W. Kamber and Ph. Tondeur, De Rham-Hodge theory for Riemannian foliations, Math. Ann.277 (1987), 415–431.
F. S. Kamber, Ph. Tondeur and G. Toth, Transversal Jacobi fields for harmonic foliations, Mich, Math, J.34 (1987), 261–266.
P. Molino, Géométrie globale des feuilletages riemanniens, Proc. Kon. Ned. Akad., A1,85 (1982), 45–76.
S. Nishikawa and Ph. Tondeur, Transversal infinitesimal automorphisms for harmonic Kähler foliations, Tôhoku Math. J.40 (1988), 599–611.
Ph. Tondeur, Foliations on Riemannian manifolds, Universitext, Springer-Verlag, Berlin-Heidlberg-New York 1988, 247 pp.
Ph. Tondeur and G. Toth, On transversal infinitesimal automorphisms for harmonic foliations, Geometriae Dedicata 24 (1987), 229–236.
S. Yorozu, The non-existence of Killing fields, Tôhoku Math. J.36 (1984), 99–105.
Author information
Authors and Affiliations
Additional information
Communicated by E. Ruh
1980 Mathematics Subject Classification: Primary 57 R 30, Secondary 58 E 20.
Work supported in part by a grant from the National Science Foundation.
Rights and permissions
About this article
Cite this article
Nishikawa, S., Tondeur, P. Transversal infinitesimal automorphisms of harmonic foliations on complete manifolds. Ann Glob Anal Geom 7, 47–57 (1989). https://doi.org/10.1007/BF00137401
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00137401