# Harmonic conformal flows on manifolds of constant curvature

Open Mathematics (2007)

- Volume: 5, Issue: 3, page 493-504
- ISSN: 2391-5455

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topAmine Fawaz. "Harmonic conformal flows on manifolds of constant curvature." Open Mathematics 5.3 (2007): 493-504. <http://eudml.org/doc/269154>.

@article{AmineFawaz2007,

abstract = {We compute the energy of conformal flows on Riemannian manifolds and we prove that conformal flows on manifolds of constant curvature are critical if and only if they are isometric.},

author = {Amine Fawaz},

journal = {Open Mathematics},

keywords = {basic form; energy; foliation; geodesic curvature; harmonic; mean curvature; projectable vector field; symmetric functions; umbilical; conformal flow; isometric flow; constant curvature},

language = {eng},

number = {3},

pages = {493-504},

title = {Harmonic conformal flows on manifolds of constant curvature},

url = {http://eudml.org/doc/269154},

volume = {5},

year = {2007},

}

TY - JOUR

AU - Amine Fawaz

TI - Harmonic conformal flows on manifolds of constant curvature

JO - Open Mathematics

PY - 2007

VL - 5

IS - 3

SP - 493

EP - 504

AB - We compute the energy of conformal flows on Riemannian manifolds and we prove that conformal flows on manifolds of constant curvature are critical if and only if they are isometric.

LA - eng

KW - basic form; energy; foliation; geodesic curvature; harmonic; mean curvature; projectable vector field; symmetric functions; umbilical; conformal flow; isometric flow; constant curvature

UR - http://eudml.org/doc/269154

ER -

## References

top- [1] D.E Blair: “Contact manifolds in Riemannian geometry”, Lect. Notes Math., Vol. 509, Springer-Verlag, Berlin-Heidelberg-New York, 1976. Zbl0319.53026
- [2] V. Borelliand F. Brito, O. Gil-Medrano: “The Infimum of The Energy of Unit Vector Fields on Odd-Dimensional Spheres”, Ann. Glob. Anal. Geom., Vol. 23 (2003), pp. 129–140. http://dx.doi.org/10.1023/A:1022404728764 Zbl1031.53090
- [3] F. Brito and P. Chacon: “Energy of Global Frames”, To appear in the J. Aust. Math. Soc..
- [4] M. Berger M. and D. Ebin, “Some decompositions of the space of symmetric tensors on a Riemannian manifold”, J. Differ. Geom., Vol. 3, (1969), pp. 379–392. Zbl0194.53103
- [5] F. Brito, R. Langevin R. and H. Rosenberg: “Intégrales de courbure sur des variétées feuilletées.”, J. Differ. Geometry, Vol. 16, (1981), pp. 19–50. Zbl0472.53049
- [6] P. Baird and J.C. Wood: “Harmonic Morphisms, Seifert Fibre Spaces and Conformal Foliations”, P. Lond. Math. Soc. Vol. 64, (1992), pp. 170–196. http://dx.doi.org/10.1112/plms/s3-64.1.170 Zbl0755.58019
- [7] Y. Carrière: “Flots Riemanniens, in “Structure Transverse des Feuilletages”, Astéerisque, Vo. 116 (1984), pp. 31–52.
- [8] J. Eells and J. Sampson: “Harmonic mappings of Riemannian manifolds”, Amer. J. Math., Vol. 86, (1964), pp. 109–160. http://dx.doi.org/10.2307/2373037 Zbl0122.40102
- [9] A. Fawaz: “Energy and Riemannian Flows”, To appear in Geometriae Dedicata. Zbl1179.53036
- [10] A. Fawaz: “Energy and Foliations on Riemann Surfaces”, Ann. Glob. Anal. Geom., Vol. 28 (2005), pp. 75–89. http://dx.doi.org/10.1007/s10455-005-4405-0 Zbl1079.53042
- [11] R. Langevin: “Feuilletages, énergies et cristaux liquides”, Astérisque Vols. 107-108, (1983), pp. 201–213. Zbl0527.53023
- [12] W. Poor: Differential Geometric Structures, McGraw Hill Book Company, New York etc. 1981.
- [13] P. Tondeur: Geometry of Foliations, Monographs in Math. Vol. 90, Birkhäuser, 1997. Zbl0905.53002
- [14] G. Wiegmink: “Total bending of vector fields on the sphere S 3”, Differ. Geome. Appl., Vol. 6, (1996), pp. 219–236 http://dx.doi.org/10.1016/0926-2245(96)82419-3
- [15] G. Wiegmink: “Total bending of vector fields on Riemannian manifolds”, Math. Ann., Vol. 303, (1995), pp. 325–344. http://dx.doi.org/10.1007/BF01460993 Zbl0834.53034
- [16] C.M. Wood: “On the energy of a unit vector field”, Geometria Dedicata, Vol. 64 (1997), pp. 319–330. http://dx.doi.org/10.1023/A:1017976425512
- [17] K. Yano: Integral Formulas in Riemannian Geometry, Marcel-Decker Inc., New York, 1970. Zbl0213.23801

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