Browse > Article
http://dx.doi.org/10.4134/BKMS.2009.46.4.713

LEFT-INVARIANT MINIMAL UNIT VECTOR FIELDS ON A LIE GROUP OF CONSTANT NEGATIVE SECTIONAL CURVATURE  

Yi, Seung-Hun (SCIENCES AND LIBERAL ARTS (MATHEMATICS) YOUNGDONG UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.46, no.4, 2009 , pp. 713-720 More about this Journal
Abstract
We find all left-invariant minimal unit vector fields and strongly normal unit vector fields on a Lie group which is isometric to the hyperbolic space.
Keywords
left-invariant minimal unit vector field; Lie group; hyperbolic manifold;
Citations & Related Records

Times Cited By Web Of Science : 1  (Related Records In Web of Science)
Times Cited By SCOPUS : 1
연도 인용수 순위
1 E. Boeckx and L. Vanhecke, Harmonic and minimal radial vector fields, Acta Math. Hungar. 90 (2001), no. 4, 317–331   DOI
2 E. Boeckx and L. Vanhecke, Harmonic and minimal vector fields on tangent and unit tangent bundles, Differential Geom. Appl. 13 (2000), no. 1, 77–93   DOI   ScienceOn
3 O. Gil-Medriano and E. Llinares-Fuster, Second variation of volume and energy of vector fields. Stability of Hopf vector fields, Math. Ann. 320 (2001), no. 3, 531–545   DOI
4 J. C. Gonzalez-Davila and L. Vanhecke, Minimal and harmonic characteristic vector fields on three-dimensional contact metric manifolds, J. Geom. 72 (2001), no. 1-2, 65–76   DOI
5 H. Gluck and W. Ziller, On the volume of a unit vector field on the three-sphere, Comment. Math. Helv. 61 (1986), no. 2, 177–192   DOI
6 D. L. Johnson, Volumes of flows, Proc. Amer. Math. Soc. 104 (1988), no. 3, 923–931
7 J. Milnor, Curvatures of left invariant metrics on Lie groups, Advances in Math. 21 (1976), no. 3, 293–329   DOI
8 S. L. Pedersen, Volumes of vector fields on spheres, Trans. Amer. Math. Soc. 336 (1993), no. 1, 69–78
9 W. A. Poor, Differential Geometric Structures, McGraw-Hill Book Co., New York, 1981
10 K. Tsukada and L. Vanhecke, Invariant minimal unit vector fields on Lie groups, Period. Math. Hungar. 40 (2000), no. 2, 123–133   DOI
11 M. Salvai, On the volume of unit vector fields on a compact semi-simple lie group, Journal of Lie Theory 13 (2003), 455–462
12 O. Gil-Medriano and E. Llinares-Fuster, Minimal unit vector fields, Tohoku Math. J. (2) 54 (2002), no. 1, 71–84   DOI
13 J. C. Gonzalez-Davila and L. Vanhecke, Examples of minimal unit vector fields, Ann. Global Anal. Geom. 18 (2000), no. 3-4, 385–404   DOI