In this paper we consider the biharmonic curves on a surface. These curves are critical points of the bienergy functional, and generalize the harmonic curves (geodesics). We first find conditions on the Gaussian curvature of the surface along a nongeodesic biharmonic curve. Then we study biharmonic curves on a surface of revolution, giving the explicit solutions in the case of surfaces of revolution with constant Gaussian curvature.
Biharmonic curves on a surface
CADDEO, RENZO ILARIO;MONTALDO, STEFANO;PIU, MARIA PAOLA
2001-01-01
Abstract
In this paper we consider the biharmonic curves on a surface. These curves are critical points of the bienergy functional, and generalize the harmonic curves (geodesics). We first find conditions on the Gaussian curvature of the surface along a nongeodesic biharmonic curve. Then we study biharmonic curves on a surface of revolution, giving the explicit solutions in the case of surfaces of revolution with constant Gaussian curvature.
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