On Constructing Biharmonic Maps and Metrics

By P. Baird, Dantouma Kamissoko. 2003

75 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7bd08884aa162c1aaeb710006c9260bde7d610c3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. C. Oniciuc
2. Stefano Montaldo
3. Ye-lin Ou
4. Eric Loubeau
5. Changyou Wang
6. A. Balmuş
7. T. Lamm
8. A. Ratto

In Astronomy and Astrophysics

1. C. Oniciuc
2. Stefano Montaldo
3. Ye-lin Ou
4. Eric Loubeau
5. Changyou Wang
6. A. Balmuş
7. A. Ratto
8. Bang‐Yen Chen

In Geometry and Topology

1. C. Oniciuc
2. Stefano Montaldo
3. Ye-lin Ou
4. Eric Loubeau
5. Changyou Wang
6. A. Balmuş
7. T. Lamm
8. Bang‐Yen Chen

Citations in the corpus

• Explicit Formulas for Non-Geodesic Biharmonic Curves of the Heisenberg Group (2003, background): “Abstract. We consider the biharmonicity condition for maps between Riemannian manifolds (see [ BK ]), and study the non-geodesic biharmonic curves in the Heisenberg group H3. First we prove that all of them are helices, and then we obtain explicitly their parametric equations.”
• Biharmonic maps from R4 into a Riemannian manifold (2004, background): “... they proposed, e.g., the problem (8.8) in page 77, the study such as existence and regularity for polyharmonic maps of order k in the critical dimension m = 2k, for k ≥ 2, analogous to those for harmonic maps in dimension 2. In contrast with extrinsic biharmonic maps, where existence can be obta”
• Some constructions of biharmonic maps and Chen's conjecture on biharmonic hypersurfaces (2009, background): “3 and the fact that φ is the graph of the inversion ψ : R(4) \ {0} −→ R(4) defined by ψ(x) = x/|x|2 which is known ([1]) to be a proper biharmonic map.”
• Biharmonic map heat flow into manifolds of nonpositive curvature (2004, unknown): “More results on intrinsic biharmonic maps, especially on the existence and non-existence of nontrivial (which means non-harmonic) intrinsic biharmonic maps can be found in [ 1 ], [2], [3], [7], [13] and [14].”
• A short survey on biharmonic maps between Riemannian manifolds (2005, background): “For l = 2 this result was first obtained in [3].”
• The stress-energy tensor for biharmonic maps (2006, background): “On Einstein manifolds, interesting links between biharmonicity of the identity (modulo a conformal change of the metric) and isoparametricity of the conformal factor have been discovered in [2,4].”