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ON TRANSVERSALLY HARMONIC MAPS OF FOLIATED RIEMANNIAN MANIFOLDS
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 Title & Authors
ON TRANSVERSALLY HARMONIC MAPS OF FOLIATED RIEMANNIAN MANIFOLDS
Jung, Min-Joo; Jung, Seoung-Dal;
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 Abstract
Let (M,F) and (M`,F`) be two foliated Riemannian manifolds with M compact. If the transversal Ricci curvature of F is nonnegative and the transversal sectional curvature of F` is nonpositive, then any transversally harmonic map is transversally totally geodesic. In addition, if the transversal Ricci curvature is positive at some point, then is transversally constant.
 Keywords
transversal tension field;transversally harmonic map;normal variational formula;generalized Weitzenbck type formula;
 Language
English
 Cited by
1.
Variation formulas for transversally harmonic and biharmonic maps, Journal of Geometry and Physics, 2013, 70, 9  crossref(new windwow)
2.
Transversally holomorphic maps between Kähler foliations, Journal of Mathematical Analysis and Applications, 2014, 416, 2, 683  crossref(new windwow)
 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. crossref(new window)

2.
J. Eells and J. H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964), 106-160.

3.
S. D. Jung, The first eigenvalue of the transversal Dirac operator, J. Geom. Phys. 39 (2001), no. 3, 253-264. crossref(new window)

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. crossref(new window)

5.
F. W. Kamber and Ph. Tondeur, Infinitesimal automorphisms and second variation of the energy for harmonic foliations, Tohoku Math. J. (2) 34 (1982), no. 4 525-538. crossref(new window)

6.
J. Konderak and R. Wolak, Transversally harmonic maps between manifolds with Riemannian foliations, Q. J. Math. 54 (2003), no. 3, 335-354. crossref(new window)

7.
J. Konderak and R. Wolak, Some remarks on transversally harmonic maps, Glasg. Math. J. 50 (2008), no. 1, 1-16.

8.
P. Molino, Riemannian Foliations, translated from the French by Grant Cairns, Boston: Birkhaser, 1988.

9.
B. O'Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 459-469. crossref(new window)

10.
H. K. Pak and J. H. Park, Transversal harmonic transformations for Riemannian foliations, Ann. Global Anal. Geom. 30 (2006), no. 1, 97-105. crossref(new window)

11.
E. Park and K. Richardson, The basic Laplacian of a Riemannian foliation, Amer. J. Math. 118 (1996), no. 6, 1249-1275. crossref(new window)

12.
H. C. J. Sealey, Harmonic maps of small energy, Bull. London Math. Soc. 13 (1981), no. 5, 405-408. crossref(new window)

13.
Ph. Tondeur, Foliations on Riemannian Manifolds, New-York, Springer-Verlag, 1988.

14.
Ph. Tondeur, Geometry of Foliations, Basel: Birkhauser Verlag, 1997.

15.
Y. L. Xin, Geometry of Harmonic Maps, Birkhauser, Boston, 1996.

16.
S. Yorozu and T. Tanemura, Green's theorem on a foliated Riemannian manifold and its applications, Acta Math. Hungar. 56 (1990), no. 3-4, 239-245. crossref(new window)