On harmonic vector fields.

Jerzy J. Konderak

Displaying similar documents to “On harmonic vector fields.”

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 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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Manifolds with strong harmonic boundaries but without Green's functions of clamped bodies

Mitsuru Nakai, Leo Sario (1976)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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On normal forms of Laplacian and its iterations in harmonic spaces

Masanori Kôzaki, Hidekichi Sumi (1989)

Commentationes Mathematicae Universitatis Carolinae

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On the biharmonicity of product maps.

Todjihounde, Leonard (2006)

International Journal of Mathematics and Mathematical Sciences

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Invariant harmonic unit vector fields on Lie groups

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

Bollettino dell'Unione Matematica Italiana

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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...