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Total bending of vector fields on Riemannian manifolds. (English) Zbl 0834.53034
The functional of total bending of globally defined unit vector fields on a Riemannian manifold is devised to measure to what extent they fail to be parallel. The total bending of such a vector field $$X$$ is essentially defined as the integral of the squared norm of the covariant differential of $$X$$. Many manifolds do not allow parallel vector fields. Aiming at finding vector fields of minimal total bending, some general variational results are derived and the situation on two-dimensional tori is investigated. In this setting rather complete results are obtained.
Reviewer: G.Wiegmink (Köln)

##### MSC:
 53C20 Global Riemannian geometry, including pinching 53A30 Conformal differential geometry (MSC2010) 58E30 Variational principles in infinite-dimensional spaces
##### Keywords:
total bending; unit vector fields; two-dimensional tori
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##### References:
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