For a noncompact harmonic manifold M we establish finite dimensionality of the eigensubspaces V-lambda generated by radial eigenfunctions of the form cosh r + c. As a consequence, for such harmonic manifolds, we give an isometric imbedding of M into (V-lambda, B), where B is a nondegenerate symmetric bilinear indefinite form on V-lambda(analogous to the imbedding of the real hyperbolic space H-n into Rn+1 with the indefinite form Q(x,x) = -x(0)(2) + Sigma x(i)(2)). This imbedding is minimal in a 'sphere' in (V-lambda, B). Finally we give certain conditions under which M is symmetric
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A harmonic morphism is a map between two Riemannian manifolds with the property that its composition...
In this paper we give a method for constructing complex valued harmonic morphisms in some pseudo-Rie...
In this paper we give a unified framework for constructing harmonic morphisms from the irreducible R...
[[abstract]]Given a complete Riemannian manifold (M, g) with nonnegative sectional curvature outside...
We show that a noncompact, complete, simply connected harmonic manifold (M-d,g) with volume density ...
[[abstract]]Let H-l(p)(M) be the space of polynomial growth harmonic forms. We proved that the dimen...
An n-dimensional Riemannian manifold is called k-harmonic for some integer k, 1 <= k <= n - 1, if th...
The Lichnerowicz conjecture asserts that all harmonic manifolds are either flat or locally symmetric...
AbstractLet X be a projective real, complex, or quaternion hyperbolic space, realized as the pseudo-...
All minimal isometric immersions of a Riemannian manifold M into a round sphere arise from eigenfunc...
AbstractAn integral representation is given for eigenfunctions of the Laplacian on a noncompact two-...
We show that any closed n-dimensional Riemannian manifold can be embedded by a map constructed from ...
This article explores and develops opportunities Fourier method of separation ofvariables for the st...
Let (S,g_0) be a hyperbolic surface, ρ be a Hitchin representation for PSL(n,R), and f be the unique...
Abstract. We show that a noncompact manifold with bounded sectional curvature, whose ends are suffic...
A harmonic morphism is a map between two Riemannian manifolds with the property that its composition...
In this paper we give a method for constructing complex valued harmonic morphisms in some pseudo-Rie...
In this paper we give a unified framework for constructing harmonic morphisms from the irreducible R...
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