JOURNAL BROWSE
Search
Advanced SearchSearch Tips
HORIZONTALLY HOMOTHETIC HARMONIC MORPHISMS AND STABILITY OF TOTALLY GEODESIC SUBMANIFOLDS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
HORIZONTALLY HOMOTHETIC HARMONIC MORPHISMS AND STABILITY OF TOTALLY GEODESIC SUBMANIFOLDS
Yun, Gab-Jin; Choi, Gun-Don;
  PDF(new window)
 Abstract
In this article, we study the relations of horizontally homothetic harmonic morphisms with the stability of totally geodesic submanifolds. Let be a horizontally homothetic harmonic morphism from a Riemannian manifold into a Riemannian manifold of non-positive sectional curvature and let T be the tensor measuring minimality or totally geodesics of fibers of . We prove that if T is parallel and the horizontal distribution is integrable, then for any totally geodesic submanifold P in N, the inverse set, (P), is volume-stable in M. In case that P is a totally geodesic hypersurface the condition on the curvature can be weakened to Ricci curvature.
 Keywords
harmonic morphism;horizontally homothetic;stable minimal submanifold;totally geodesic;
 Language
English
 Cited by
1.
Stability and integrability of horizontally conformal maps and harmonic morphisms, Mathematische Nachrichten, 2013, n/a  crossref(new windwow)
 References
1.
P. Baird and J. Eells, A Conservation Law for Harmonic Maps, Geometry Symposium, Utrecht 1980 (Utrecht, 1980), pp. 1-25, Lecture Notes in Math., 894, Springer, Berlin-New York, 1981

2.
P. Baird and S. Gudmundsson, p-harmonic maps and minimal submanifolds, Math. Ann. 294 (1992), no. 4, 611-624 crossref(new window)

3.
G. D. Choi and Gabjin Yun, Harmonic morphisms and stable minimal submanifolds, Preprint

4.
B. Fuglede, Harmonic morphisms between Riemannian manifolds, Ann. Inst. Fourier (Grenoble) 28 (1978), no. 2, vi, 107-144

5.
S. Gudmundsson, The Geometry of Harmonic Morphisms, Ph. D Thesis, 1992

6.
T. Ishihara, A mapping of Riemannian manifolds which preserves harmonic functions, J. Math. Kyoto Univ. 19 (1979), no. 2, 215-229

7.
A. Kasue and T. Washio, Growth of equivariant harmonic maps and harmonic morphisms, Osaka J. Math. 27 (1990), no. 4, 899-928

8.
H. B. Lawson, Lectures on Minimal Submanifolds. Vol. I. Second edition. Mathematics Lecture Series, 9. Publish or Perish, Inc., Wilmington, Del., 1980

9.
E. Loubeau, On p-harmonic morphisms, Differential Geom. Appl. 12 (2000), no. 3, 219-229 crossref(new window)

10.
S. Montaldo, Stability of harmonic morphisms to a surface, Internat. J. Math. 9 (1998), no. 7, 865-875 crossref(new window)

11.
B. O'Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 459-469 crossref(new window)