Displaying similar documents to “On normal forms of Laplacian and its iterations in harmonic spaces”

Embedding of open riemannian manifolds by harmonic functions

Robert E. Greene, H. Wu (1975)

Annales de l'institut Fourier

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Let M be a noncompact Riemannian manifold of dimension n . Then there exists a proper embedding of M into R 2 n + 1 by harmonic functions on M . It is easy to find 2 n + 1 harmonic functions which give an embedding. However, it is more difficult to achieve properness. The proof depends on the theorems of Lax-Malgrange and Aronszajn-Cordes in the theory of elliptic equations.

On harmonic vector fields.

Jerzy J. Konderak (1992)

Publicacions Matemàtiques

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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.