DOI QR코드

DOI QR Code

New Methods of Construction for Biharmonic Maps

  • Received : 2017.12.31
  • Accepted : 2018.10.16
  • Published : 2019.03.23

Abstract

In this paper we study some properties of Riemannian manifolds, we construct a new example of non-harmonic biharmonic maps, and we characterize the biharmonicity of some curves on Riemannian manifolds.

Keywords

References

  1. P. Baird and D. Kamissoko, On constructing biharmonic maps and metrics, Ann. Global Anal. Geom., 23(1)(2003), 65-75. https://doi.org/10.1023/A:1021213930520
  2. P. Baird and J. C. Wood, Harmonic morphisms between Riemannain manifolds, Clarendon Press, Oxford, 2003.
  3. R. Caddeo and S. Montaldo, C. Oniciuc, Biharmonic submanifolds of ${\mathbb{S}}^3$, Int. J. Math., 12(2001), 867-876. https://doi.org/10.1142/S0129167X01001027
  4. J. Eells and J. H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math., 86(1964), 109-160. https://doi.org/10.2307/2373037
  5. G. Y. Jiang, 2-harmonic maps and their first and second variational formulas, Chinese Ann. Math. Ser. A, 7(4)(1986), 389-402.
  6. B. O'Neil, Semi-Riemannian geometry, Academic Press, New York, 1983.
  7. T. Sakai, Riemannian geometry, Shokabo, Tokyo, 1992 (in Japanse).
  8. Y. Xin, Geometry of harmonic maps, Fudan University, 1996.