ENERGY OF GLOBAL FRAMES

Author(s)

Brito, Fabiano G. B. ^[1] ; Chacon, Pablo M. ^[2]

Affiliation

^[1] Univ Sao Paulo, Dept Matemat, Inst Matemat & Estatist, BR-05508090 Sao Paulo - Brazil

^[2] Univ Salamanca, Fac Ciencias, Dept Matemat, E-37008 Salamanca - Spain

• Document type: Journal article
• Source: JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY; v. 84, n. 2, p. 155-162, APR 2008.
• Web of Science Citations: 0

Abstract

The energy of a unit vector field X on a closed Riemannian manifold M is defined as the energy of the section into T(1) M determined by X. For odd-dimensional spheres, the energy functional has an infimum for each dimension 2k + 1 which is not attained by any non-singular vector field for k > 1. For k = 1, Hopf vector fields are the unique minima. In this paper we show that for any closed Riemannian manifold, the energy of a frame defined on the manifold, possibly except on a finite subset, admits a lower bound in terms of the total scalar curvature of the manifold. In particular, for odd-dimensional spheres this lower bound is attained by a family of frames defined on the sphere minus one point and consisting of vector fields parallel along geodesics. (AU)

• FAPESP's process: 99/02684-5 - Geometry and Topology of Riemannian Manifolds
• Grantee: Fabiano Gustavo Braga Brito
• Support Opportunities: Research Projects - Thematic Grants