Open Access
Subscription Access
Open Access
Subscription Access
New Types of Metrics Deformations and Applications to p-Biharmonic Maps
Subscribe/Renew Journal
We construct p-biharmonic non p-harmonic maps between Riemannian manifolds (M, g) and (N, h) by first making the ansatz that φ : (M, g) → (N, h) be a p-biharmonic map and then deforming the metric on N by h˜ = h − df ⊗ df to render φ p-biharmonic, where f is a smooth function on N satisfying some conditions. We construct a new example of p-biharmonic non p-harmonic map.
Keywords
p-Harmonic Maps, p-Biharmonic Maps.
Subscription
Login to verify subscription
User
Font Size
Information
- P. Baird, A. Fardoun and S. Ouakkas, Conformal and semi-conformal biharmonic maps, Ann. Glob. Anal. Geom., 34 (4)(2008), 403 - 414.
- P. Baird and D. Kamissoko, On constructing biharmonic maps and metrics, Ann. Global Anal. Geom., 23 (1)(2003), 65 - 75.
- P. Baird and J. C. Wood, Harmonic morphisms between Riemannain manifolds, Clarendon Press, Oxford, 2003.
- P. Baird and S. Gudmundsson, p-Harmonic maps and minimal submanifolds, Math. Ann., 294 (1992), 611 - 624.
- A. Benkartab and A. Mohammed Cherif, New methods of construction for biharmonic maps, Kyungpook Math. J., 59 (2019), 135 - 147.
- A. Benkartab and A. Mohammed Cherif, Deformations of Metrics and Biharmonic Maps, Communications in Mathematics, 28 (2020), 263 - 275.
- B. Bojarski and T. Iwaniec, p-Harmonic equation and quasiregular mappings, Banach Center Publ., 19 (1)(1987), 25 - 38.
- J. Eells and J. H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math., 86 (1964), 109 - 160.
- A. Fardoun, On equivariant p-harmonic maps, Ann.Inst. Henri. Poincare, 15 (1998), 25 - 72.
- G. Y. Jiang, 2-harmonic maps and their first and second variational formulas, Chinese Ann. Math. Ser. A., 7 (4)(1986), 389 - 402.
- A. Mohammed Cherif, On the p-harmonic and p-biharmonic maps, J. Geom., 109 (41)(2018).
- C. Oniciuc, New examples of biharmonic maps in spheres, Colloq. Math., 97 (2003), 131 - 139.
- S. Ouakkas, Biharmonic maps, conformal deformations and the Hopf maps, Differential Geometry and its Applications, 26 (2008), 495 - 502.
- B. O’Neil, Semi- Riemannian Geometry, Academic Press, New York, 1983.
- C. Udri¸ste, Convex Functions and Optimization Methods on Riemannian Manifolds, Mathematics and Its Applications, Kluwer Academic Publishers: Dordrecht, The Netherlands, 1994.
- Y. Xin, Geometry of harmonic maps, Fudan University, 1996.
Abstract Views: 263
PDF Views: 0