On Polyharmonic Riemannian Manifolds
Copyright policy )On Polyharmonic Riemannian Manifolds
A natural generalization of the harmonic manifolds is considered: a Riemannian manifold is called k -harmonic or polyharmonic if it admits a non-constant k -harmonic function depending only on the geodesic distance r = r(x, y) or rather on Synge’s function \sigma = \sigma (x, y) , i.e. a solution F of \Delta^k F(\sigma) = 0 . Certain theorems are generalized from harmonic to polyharmonic manifolds.
- University of Greifswald Germany
- University of Opole Poland
Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics, pseudo-Riemannian manifold, polyharmonic function, k-harmonic space, Synge's two-point function, iterated Laplacian
Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics, pseudo-Riemannian manifold, polyharmonic function, k-harmonic space, Synge's two-point function, iterated Laplacian
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