Stability of F-biharmonic maps

Document Type : Research Paper


Department of Mathematics and Computer Science‎, ‎Amirkabir University of Technology‎, ‎Tehran‎, ‎Iran.


This paper studies some properties of F-biharmonic maps between Riemannian manifolds. By considering the first variation formula of the F-bienergy functional, F-biharmonicity of conformal maps are investigated. Moreover, the second variation formula for F-biharmonic maps is obtained. As an application, instability and nonexistence theorems for F-biharmonic maps are given.


Main Subjects

M. Ara, Instability and nonexistence theorems for F-harmonic maps, Illinois J. Math. 45 (2001), no. 2, 657--679.
M. Ara, Stability of F-harmonic maps into pinched manifolds, Hiroshima Math. J. 31 (2001), no. 1, 171--181.
P. Baird, A. Fardoun and S. Ouakkas, Conformal and semi-conformal biharmonic maps, Ann. Global Anal. Geom. 34 (2008) 403--414.
P. Baird and J.C.Wood, Harmonic Morphisms Between Riemannian Manifolds, London Math. Soc. Monogr. Ser. 29, Oxford Univ. Pres, 2003.
A. Balmus, S. Montaldoa and C. Oniciuc, Biharmonic maps between warped product manifolds, J. Geom. Phys. 57 (2007), no. 2, 449--466.
R. Caddeo, S. Montaldo and C. Oniciuc, Biharmonic submanifolds in spheres, Israel J. Math. 130 (2002) 109--123.
R.M. El-Ashwah and M.K. Aouf, A certain convolution approach for subclasses of univalent harmonic functions, Bull. Iranian Math. Soc. 41 (2015), no. 3, 739-748.
J. Eells and L. Lemaire, Selected Topics in Harmonic Maps, CBMS Regional Conference Series in Mathematics, 50, Amer. Math. Soc. Providence, RI, 1983, 85 pages.
J. Eells and J.H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964), no. 2, 109--160.
J. Eells and J.C. Wood, Restrictions on harmonic maps of surfaces, Topology 15 (1976), no. 3, 263--266.
Y.B. Han, Some results of p-biharmonic submanifolds in a Riemannian manifold of non-positive curvature, J. Geom. 106 (2015), no. 3, 471--482.
Y.B. Han and S.X. Feng, Some results of F-biharmonic maps, Acta Math. Univ. Comenian. (N.S.) 83 (2014), no. 1, 47--66.
Y.B. Han and W. Zhang, Some results of p-biharmonic maps into a non-positively curved manifold, J. Korean Math. Soc. 52 (2015), no. 5, 1097--1108.
G.Y. Jiang, 2-harmonic maps and their first and second variation formulas, Note Mat.28 (2008) 209--232.
J. Li, Stable exponentially harmonic maps between Finsler manifolds, Bull. Iranian Math. Soc. 36 (2010), no. 2, 185--207.
C. Oniciuc, On the second variation formula for biharmonic maps to a sphere, Publ Math. Debrecen. 61 (2002), no. 3-4, 613--622.
J. Qiao, J. Chen and M. Shi, On certain subclasses of univalent p-harmonic mappings, Bull. Iranian Math. Soc. 41 (2015), no. 2, 429--451.
T. Sakai, On Riemannian manifolds admitting a function whose gradient is of constant norm, Kodai Math. J. 19 (1996), no. 1, 39--51.
Volume 43, Issue 6
November 2017
Pages 1657-1669
  • Receive Date: 21 January 2016
  • Revise Date: 29 August 2016
  • Accept Date: 30 August 2016
  • First Publish Date: 30 November 2017