On normal forms of Laplacian and its iterations in harmonic spaces

Masanori Kôzaki; Hidekichi Sumi

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

On mean value theorems for small geodesic spheres in Riemannian manifolds

Masanori Kôzaki (1992)

Czechoslovak Mathematical Journal

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On the harmonic and Killing tensor field on a compact Riemannian manifold.

Tsagas, Gr., Bitis, Gr. (2001)

Balkan Journal of Geometry and its Applications (BJGA)

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Harmonic morphisms and subharmonic functions.

Choi, Gundon, Yun, Gabjin (2005)

International Journal of Mathematics and Mathematical Sciences

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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.