The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “On the energy of sections of trivializable sphere bundles.”

Invariant harmonic unit vector fields on Lie groups

J. C. González-Dávila, L. Vanhecke (2002)

Bollettino dell'Unione Matematica Italiana

Similarity:

We provide a new characterization of invariant harmonic unit vector fields on Lie groups endowed with a left-invariant metric. We use it to derive existence results and to construct new examples on Lie groups equipped with a bi-invariant metric, on three-dimensional Lie groups, on generalized Heisenberg groups, on Damek-Ricci spaces and on particular semi-direct products. In several cases a complete list of such vector fields is given. Furthermore, for a lot of the examples we determine...

Conjugacy of normally tangent diffeomorphisms : a tool for treating moduli of stability

Patrick Bonckaert (1990)

Annales de l'institut Fourier

Similarity:

We give sufficient conditions for the conjugacy of two diffeomorphisms coinciding on a common invariant submanifold V and with equal normal derivative; moreover we obtain that the homeomorphism h realizing this conjugacy satisfies additional inequalities. These inequalities, implying also the existence of the normal derivative of h along V, serve to extend this conjugacy towards regions where moduli of stability are present.

On harmonic vector fields.

Jerzy J. Konderak (1992)

Publicacions Matemàtiques

Similarity:

A tangent bundle to a Riemannian manifold carries various metrics induced by a Riemannian tensor. We consider harmonic vector fields with respect to some of these metrics. We give a simple proof that a vector field on a compact manifold is harmonic with respect to the Sasaki metric on TM if and only if it is parallel. We also consider the metrics and on a tangent bundle (cf. [YI]) and harmonic vector fields generated by them.