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dg-ga1996
A Pinching constant for harmonic manifolds
K. Ramachandran, Akhil Ranjan
In this note we shall show that the sectional curvature of a harmonic manifold is bounded on both sides. In fact we shall give a pinching constant for all harmonic manifolds. We sh…
dg-ga1996
Harmonic manifolds with some specific volume densities
K. Ramachandran, Akhil Ranjan
We show that noncompact simply connected harmonic manifolds with volume density is isometric to the real hyperbolic space and noncompact simply connected…
dg-ga1996
Finite dimensional imbeddings of harmonic spaces
K. Ramachandran, Akhil Ranjan
In a noncompact harmonic manifold we establish finite dimensionality of the eigenspaces generated by radial eigenfunctions of the form . As a consequence, fo…