• Jung, Seoung Dal (Department of Mathematics and Research Institute for Basic Sciences, Jeju National University)
  • Received : 2014.08.04
  • Accepted : 2014.09.11
  • Published : 2014.12.25


In this article, we study the transverse Killing forms with finite global norms on complete foliated Riemannian manifolds.


transverse Killing form;transversal Killing vector field


Supported by : Jeju National University


  1. J. A. Alvarez Lopez, The basic component of the mean curvature of Riemannian foliations, Ann. Global Anal. Geom. 10 (1992), 179-194.
  2. T. Aoki and S. Yorozu, $L^2$-transverse conformal and Killing fields on complete foliated Riemannian manifolds, Yokohama Math. J. 36 (1988), 27-41.
  3. P. Berard, A note on Bochner type theorems for complete manifolds, Manuscripta Math. 69 (1990), 261-266.
  4. S. D. Jung, The first eigenvalue of the transversal Dirac operator, J. Geom. Phys. 39 (2001), 253-264.
  5. S. D. Jung, Eigenvalue estimates for the basic Dirac operator on a Riemannian foliation admitting a basic harmonic 1-form, J. Geom. Phys. 57 (2007), 1239- 1246.
  6. M. J. Jung and S. D. Jung, Liouville type theorem for transversally harmonic maps, arXiv:1307.3627v2[math.DG] 29 Aug 2014.
  7. S. D. Jung and M. J. Jung, Transverse Killing forms on a Kahler foliation, Bull. Korean Math. Soc. 49 (2012), 445-454.
  8. S. D. Jung and K. Richardson, Transverse conformal Killing forms and a Gallot-Meyer theorem for foliations, Math. Z. 270 (2012), 337-350.
  9. F. W. Kamber and Ph. Tondeur, Infinitesimal automorphisms and second variation of the energy for harmonic foliations, Tohoku Math. J. 34 (1982), 525-538.
  10. F. W. Kamber and Ph. Tondeur, De Rham-Hodge theory for Riemannian foliations, Math. Ann. 277 (1987), 415-431.
  11. T. Kashiwada, On conformal Killing tensor, Natur. Sci. Rep. Ochanomizu Univ. 19 (1968), 67-74.
  12. T. Kashiwada and S. Tachibana, On the integrability of Killing-Yano's equation, J. Math. Soc. Japan 21 (1969), 259-265.
  13. P. Molino, Riemannian foliations, translated from the French by Grant Cairns, Boston: Birkhaser, 1988.
  14. S. Nishikawa and Ph. Tondeur, Transversal infinitesimal automorphisms of harmonic foliations on complete manifolds, Anal. Global Anal. Geom. 7 (1989), 47-57.
  15. J. S. Pak and S. D. Jung, A transversal Dirac operator and some vainshing theorems on a complete foliated Riemannian manifold, Math. J. Toyama Univ. 16 (1993), 97-108.
  16. J. S. Pak and S. Yorozu, Transverse fields on foliated Riemannian manifolds, J. Korean Math. Soc. 25 (1988), 83-92.
  17. E. Park and K. Richardson, The basic Laplacian of a Riemannian foliation, Amer. J. Math. 118 (1996), 1249-1275.
  18. Ph. Tondeur, Geometry of foliations, Basel: Birkhauser Verlag, 1997.
  19. K. Yano, Some remarks on tensor fields and curvature, Ann. Math. 55 (1952), 328-347.
  20. S. Yorozu, Conformal and Killing vector fields on complete non-compact Riemannian manifolds, Geometry of geodesics and related topics, Advanced Studies in Pure Mathematics 3 (1984).
  21. S. Yorozu, Killing vector fields on complete Riemannian manifolds, Proc. Amer. Math. Soc. 84 (1982), 115-120.
  22. S. Yorozu, The non-existence of Killing fields, Tohoku Math. J. 36 (1984), 99-105.

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