Total bending of flows with mean curvature correction

✍ Scribed by Fabiano G.B. Brito

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 46 KB
• Volume: 12
• Category: Article
• ISSN: 0926-2245
• DOI: 10.1016/s0926-2245(00)00007-3

✦ Synopsis

We prove in this paper that Hopf flows in S 3 are absolute minima of the total bending functional B introduced by G. Wiegmink. They are also absolute minima of the energy functional E introduced by C.M. Wood, once E differs from B by a constant. In fact, we introduce a functional D for a flow on a closed n-dimensional Riemannian manifold M which, in the three dimensional case, coincides with B up to normalization and prove that D is absolutely minimized by Hopf flows on odd-dimensional unit spheres. We also provide an extension of a theorem proven by H. Gluck and W. Ziller about volume of vector fields on S 3 .