The notion of k-harmonic curves is associated with the kth-order variational problem defined by the k-energy functional. The present paper gives a geometric formulation of this higher-order variational problem on a Riemannian manifold M and describes a g
In this maner, the integral surface will be tangent to a specified vertex cone P 0 with the curve, whose direction vector line is given by ( a 1 , a 2 , z 1 a 1 + z 2 a 1 ) (Figure 3). Figure 3. (a) Monge Cone and its forming planes. (b) Field of cones on the ...