Research Article
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Biharmonic maps on kenmotsu manifolds

Year 2016, Volume: 4 Issue: 3, 129 - 139, 30.09.2016
https://izlik.org/JA97UA85GL

Abstract




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




References

  • 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.

Year 2016, Volume: 4 Issue: 3, 129 - 139, 30.09.2016
https://izlik.org/JA97UA85GL

Abstract

References

  • 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.
There are 21 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Abdelkader Zagane This is me

Seddik Ouakkas This is me

Publication Date September 30, 2016
IZ https://izlik.org/JA97UA85GL
Published in Issue Year 2016 Volume: 4 Issue: 3

Cite

APA Zagane, A., & Ouakkas, S. (2016). Biharmonic maps on kenmotsu manifolds. New Trends in Mathematical Sciences, 4(3), 129-139. https://izlik.org/JA97UA85GL
AMA 1.Zagane A, Ouakkas S. Biharmonic maps on kenmotsu manifolds. New Trends in Mathematical Sciences. 2016;4(3):129-139. https://izlik.org/JA97UA85GL
Chicago Zagane, Abdelkader, and Seddik Ouakkas. 2016. “Biharmonic Maps on Kenmotsu Manifolds”. New Trends in Mathematical Sciences 4 (3): 129-39. https://izlik.org/JA97UA85GL.
EndNote Zagane A, Ouakkas S (September 1, 2016) Biharmonic maps on kenmotsu manifolds. New Trends in Mathematical Sciences 4 3 129–139.
IEEE [1]A. Zagane and S. Ouakkas, “Biharmonic maps on kenmotsu manifolds”, New Trends in Mathematical Sciences, vol. 4, no. 3, pp. 129–139, Sept. 2016, [Online]. Available: https://izlik.org/JA97UA85GL
ISNAD Zagane, Abdelkader - Ouakkas, Seddik. “Biharmonic Maps on Kenmotsu Manifolds”. New Trends in Mathematical Sciences 4/3 (September 1, 2016): 129-139. https://izlik.org/JA97UA85GL.
JAMA 1.Zagane A, Ouakkas S. Biharmonic maps on kenmotsu manifolds. New Trends in Mathematical Sciences. 2016;4:129–139.
MLA Zagane, Abdelkader, and Seddik Ouakkas. “Biharmonic Maps on Kenmotsu Manifolds”. New Trends in Mathematical Sciences, vol. 4, no. 3, Sept. 2016, pp. 129-3, https://izlik.org/JA97UA85GL.
Vancouver 1.Abdelkader Zagane, Seddik Ouakkas. Biharmonic maps on kenmotsu manifolds. New Trends in Mathematical Sciences [Internet]. 2016 Sep. 1;4(3):129-3. Available from: https://izlik.org/JA97UA85GL