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2007 | 5 | 3 | 493-504
Tytuł artykułu

Harmonic conformal flows on manifolds of constant curvature

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
5
Numer
3
Strony
493-504
Opis fizyczny
Daty
wydano
2007-09-01
online
2007-09-01
Twórcy
autor
  • The University of Texas of the Permian Basin, 4901 East University, fawaz_a@utpb.edu
Bibliografia
  • [1] D.E Blair: “Contact manifolds in Riemannian geometry”, Lect. Notes Math., Vol. 509, Springer-Verlag, Berlin-Heidelberg-New York, 1976.
  • [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
  • [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.
  • [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.
  • [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
  • [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
  • [9] A. Fawaz: “Energy and Riemannian Flows”, To appear in Geometriae Dedicata.
  • [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
  • [11] R. Langevin: “Feuilletages, énergies et cristaux liquides”, Astérisque Vols. 107-108, (1983), pp. 201–213.
  • [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.
  • [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
  • [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-007-0020-6
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