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Biharmonic maps on kenmotsu manifolds

Yıl 2016, Cilt: 4 Sayı: 3, 129 - 139, 30.09.2016

Öz




In this paper we study biharmonic maps on Kenmotsu manifolds.
An example for biharmonic map of a three-Kenmotsu manifold is constructed for
illustration.




Kaynakça

  • P. Baird, Harmonic maps with symmetry, harmonic morphisms and deformation of metrics, Pitman Books Limited, 27-39, (1983).
  • P. Baird and J. Eells, A conservation law for harmonic maps, Lecture Notes in Math. 894, Springer, 1-25, (1981).
  • P.Baird, A. Fardoun and S. Ouakkas, Conformal and semi-conformal biharmonic maps, Ann. Glob Anal Geom 34, 403-414 (2008).
  • P. Baird and D. Kamissoko, On constructing biharmonic maps and metrics, Annals of Global Analysis and Geometry 23, 65-75, (2003).
  • P. Baird and J.C. Wood, Harmonic morphisms between Riemannain manifolds, Oxford Sciences Publications (2003).
  • A. Balmus, Biharmonic properties and conformal changes, An. Stiint. Univ. Al.I. Cuza Iasi Mat. (N.S.) 50, 367-372, (2004).
  • D.E. Blair, Riemannian geometry of contact and Symplectic Manifolds, Birkhauser. Boston, Second Edition (2010).
  • U.C.De and G. Pathok, On 3-dimensional Kenmotsu manifolds, Indian J. Pure Appl. Math. 35, 159-165, (2004).
  • J. Eells and L. Lemaire, A report on harmonic maps, Bull. London Math. Soc. 16, 1-68, (1978).
  • J. Eells and L. Lemaire, Another report on harmonic maps, Bull. London Math. Soc. 20, 385-524, (1988).
  • J. Eells and L. Lemaire, Selected topics in harmonic maps, CNMS Regional Conference Series of the National Sciences Foundation, November 1981.
  • J. Eells and A. Ratto, Harmonic Maps and Minimal Immersions with Symmetries, Princeton University Press 1993.
  • G. Y. Jiang, 2-harmonic maps and their first and second variational formulas, Chinese Ann. Math. Ser. A 7, 389-402, (1986).
  • J.B Jun, U.C. De and G. Pathak, On Kenmotsu Manifolds, J. Korean Math. Soc. 42, No. 3, 435-445, (2005).
  • K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J. II Ser. 24, 93-103, (1972).
  • A. Najma, Harmonic Maps on Kenmotsu Manifolds, An. St. Univ. Ovidius Constanta. Vol. 21(3), 197-208, 2013.
  • C. Oniciuc, New examples of biharmonic maps in spheres, Colloq. Math., 97, 131-139, (2003).
  • Ouakkas, S, Biharmonic maps, conformal deformations and the Hopf maps, Diff. Geom. Appl, 26, 495-502, (2008).
  • Y.-L. Ou, p-harmonic morphisms, biharmonic morphisms, and non-harmonic biharmonic maps, J. Geom. Phys. Volume 56, 3, 358-374, (2006).
  • G. Pitis¸, Geometry of Kenmotsu manifolds, Publishing House of Transilvania University of Bra¸sov, Bra¸sov, (2007).
  • K. Yano and M. Kon, Structures on manifolds, vol. 3, Series in pure Math., World Scientifc, Singapore, 1984.
Yıl 2016, Cilt: 4 Sayı: 3, 129 - 139, 30.09.2016

Öz

Kaynakça

  • P. Baird, Harmonic maps with symmetry, harmonic morphisms and deformation of metrics, Pitman Books Limited, 27-39, (1983).
  • P. Baird and J. Eells, A conservation law for harmonic maps, Lecture Notes in Math. 894, Springer, 1-25, (1981).
  • P.Baird, A. Fardoun and S. Ouakkas, Conformal and semi-conformal biharmonic maps, Ann. Glob Anal Geom 34, 403-414 (2008).
  • P. Baird and D. Kamissoko, On constructing biharmonic maps and metrics, Annals of Global Analysis and Geometry 23, 65-75, (2003).
  • P. Baird and J.C. Wood, Harmonic morphisms between Riemannain manifolds, Oxford Sciences Publications (2003).
  • A. Balmus, Biharmonic properties and conformal changes, An. Stiint. Univ. Al.I. Cuza Iasi Mat. (N.S.) 50, 367-372, (2004).
  • D.E. Blair, Riemannian geometry of contact and Symplectic Manifolds, Birkhauser. Boston, Second Edition (2010).
  • U.C.De and G. Pathok, On 3-dimensional Kenmotsu manifolds, Indian J. Pure Appl. Math. 35, 159-165, (2004).
  • J. Eells and L. Lemaire, A report on harmonic maps, Bull. London Math. Soc. 16, 1-68, (1978).
  • J. Eells and L. Lemaire, Another report on harmonic maps, Bull. London Math. Soc. 20, 385-524, (1988).
  • J. Eells and L. Lemaire, Selected topics in harmonic maps, CNMS Regional Conference Series of the National Sciences Foundation, November 1981.
  • J. Eells and A. Ratto, Harmonic Maps and Minimal Immersions with Symmetries, Princeton University Press 1993.
  • G. Y. Jiang, 2-harmonic maps and their first and second variational formulas, Chinese Ann. Math. Ser. A 7, 389-402, (1986).
  • J.B Jun, U.C. De and G. Pathak, On Kenmotsu Manifolds, J. Korean Math. Soc. 42, No. 3, 435-445, (2005).
  • K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J. II Ser. 24, 93-103, (1972).
  • A. Najma, Harmonic Maps on Kenmotsu Manifolds, An. St. Univ. Ovidius Constanta. Vol. 21(3), 197-208, 2013.
  • C. Oniciuc, New examples of biharmonic maps in spheres, Colloq. Math., 97, 131-139, (2003).
  • Ouakkas, S, Biharmonic maps, conformal deformations and the Hopf maps, Diff. Geom. Appl, 26, 495-502, (2008).
  • Y.-L. Ou, p-harmonic morphisms, biharmonic morphisms, and non-harmonic biharmonic maps, J. Geom. Phys. Volume 56, 3, 358-374, (2006).
  • G. Pitis¸, Geometry of Kenmotsu manifolds, Publishing House of Transilvania University of Bra¸sov, Bra¸sov, (2007).
  • K. Yano and M. Kon, Structures on manifolds, vol. 3, Series in pure Math., World Scientifc, Singapore, 1984.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Abdelkader Zagane Bu kişi benim

Seddik Ouakkas Bu kişi benim

Yayımlanma Tarihi 30 Eylül 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 4 Sayı: 3

Kaynak Göster

APA Zagane, A., & Ouakkas, S. (2016). Biharmonic maps on kenmotsu manifolds. New Trends in Mathematical Sciences, 4(3), 129-139.
AMA Zagane A, Ouakkas S. Biharmonic maps on kenmotsu manifolds. New Trends in Mathematical Sciences. Eylül 2016;4(3):129-139.
Chicago Zagane, Abdelkader, ve Seddik Ouakkas. “Biharmonic Maps on Kenmotsu Manifolds”. New Trends in Mathematical Sciences 4, sy. 3 (Eylül 2016): 129-39.
EndNote Zagane A, Ouakkas S (01 Eylül 2016) Biharmonic maps on kenmotsu manifolds. New Trends in Mathematical Sciences 4 3 129–139.
IEEE A. Zagane ve S. Ouakkas, “Biharmonic maps on kenmotsu manifolds”, New Trends in Mathematical Sciences, c. 4, sy. 3, ss. 129–139, 2016.
ISNAD Zagane, Abdelkader - Ouakkas, Seddik. “Biharmonic Maps on Kenmotsu Manifolds”. New Trends in Mathematical Sciences 4/3 (Eylül 2016), 129-139.
JAMA Zagane A, Ouakkas S. Biharmonic maps on kenmotsu manifolds. New Trends in Mathematical Sciences. 2016;4:129–139.
MLA Zagane, Abdelkader ve Seddik Ouakkas. “Biharmonic Maps on Kenmotsu Manifolds”. New Trends in Mathematical Sciences, c. 4, sy. 3, 2016, ss. 129-3.
Vancouver Zagane A, Ouakkas S. Biharmonic maps on kenmotsu manifolds. New Trends in Mathematical Sciences. 2016;4(3):129-3.