TRANSVERSE KILLING FORMS ON A KÄAHLER FOLIATION

Title & Authors
TRANSVERSE KILLING FORMS ON A KÄAHLER FOLIATION
Jung, Seoung-Dal; Jung, Min-Joo;

Abstract
On a closed, connected Riemannian manifold with a K$\small{\ddot{a}}$ahler foliation $\small{\mathcal{F}}$ of codimension $\small{q}$, any transverse Killing $\small{r}$-form ($\small{2{\leq}r{\leq}q}$) is parallel.
Keywords
transverse Killing form;transverse conformal Killing form;K$\small{\ddot{a}}$ahler foliation;
Language
English
Cited by
1.
TRANSVERSE KILLING FORMS ON COMPLETE FOLIATED RIEMANNIAN MANIFOLDS,;

호남수학학술지, 2014. vol.36. 4, pp.731-737
1.
TRANSVERSE KILLING FORMS ON COMPLETE FOLIATED RIEMANNIAN MANIFOLDS, Honam Mathematical Journal, 2014, 36, 4, 731
2.
Transverse conformal Killing forms on Kähler foliations, Journal of Geometry and Physics, 2015, 90, 29
3.
$$L^\mathrm{2}$$ L 2 -transverse conformal Killing forms on complete foliated manifolds, Mathematische Zeitschrift, 2017
References
1.
J. A. Alvarez Lopez, The basic component of the mean curvature of Riemannian foliations, Ann. Global Anal. Geom. 10 (1992), no. 2, 179-194.

2.
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), no. 4, 1239-1246.

3.
M. J. Jung and S. D. Jung, Riemannian foliations admitting transversal conformal fields, Geom. Dedicata 133 (2008), 155-168.

4.
S. D. Jung, K. R. Lee, and K. Richardson, Generalized Obata theorem and its applications on foliations, J. Math. Anal. Appl. 376 (2011), no. 1, 129-135.

5.
S. D. Jung and K. Richardson, Transverse conformal Killing forms and a Gallot-Meyer Theorem for foliations, Math. Z. 270 (2012), 337-350.

6.
F. W. Kamber and Ph. Tondeur, Harmonic foliations, Proc. National Science Foundation Conference on Harmonic Maps, 87-121, Tulance, Dec. 1980, Lecture Notes in Math. 949, Springer-Verlag, New York, 1982.

7.
F. W. Kamber and Ph. Tondeur, Infinitesimal automorphisms and second variation of the energy for harmonic foliations, Tohoku Math. J. 34 (1982), no. 2, 525-538.

8.
F. W. Kamber and Ph. Tondeur, De Rham-Hodge theory for Riemannian foliations, Math. Ann. 277 (1987), no. 3, 415-431.

9.
T. Kashiwada and S. Tachibana, On the integrability of Killing-Yano's equation, J. Math. Soc. Japan 21 (1969), 259-265.

10.
M. Min-Oo, E. A. Ruh, and Ph. Tondeur, Vanishing theorems for the basic cohomology of Riemannian foliations, J. Reine Angew. Math. 415 (1991), 167-174.

11.
A. Moroianu and U. Semmelmann, Twistor forms on Kahler manifolds, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 2 (2003), no. 4, 823-845.

12.
S. Nishikawa, Ph. Tondeur, Transversal infinitesimal automorphisms for harmonic Kahler foliations, Tohoku Math. J. 40 (1988), no. 4, 599-611.

13.
J. S. Pak and S. Yorozu, Transverse fields on foliated Riemannian manifolds, J. Korean Math. Soc. 25 (1988), no. 1, 83-92.

14.
E. Park and K. Richardson, The basic Laplacian of a Riemannian foliation, Amer. J. Math. 118 (1996), no. 6, 1249-1275.

15.
U. Semmelmann, Conformal Killing forms on Riemannian manifolds, Math. Z. 245 (2003), no. 3, 503-527.

16.
S. Tachibana, On conformal Killing tensor in a Riemannian space, Tohoku Math. J. 21 (1969), 56-64.

17.
S. Tachibana, On Killing tensors in Riemannian manifolds of positive curvature operator, Tohoku Math. J. 28 (1976), 177-184.

18.
Ph. Tondeur, Foliations on Riemannian Manifolds, Springer-Verlag, New-York, 1988.

19.
Ph. Tondeur, Geometry of Foliations, Birkhauser-Verlag, Basel; Boston; Berlin, 1997.

20.
K. Yano, Some remarks on tensor fields and curvature, Ann. of Math. 55 (1952), 328- 347.