Title : Fundamental solutions of the Helmholtz operator on Riemannian spaces of constant curvature and their Gegenbauer expansions
Speaker: Dr Howard Cohl
Affiliation: National Institute of Standards and Technology, USA
Time: 14:00 Monday, 5 February, 2018
Location: 303E-257
We compute closed-form expressions for oscillatory and damped spherically symmetric fundamental solutions of the Helmholtz equation in hyperbolic and hyperspherical geometry. We are using the R-radius hypersphere and the R-radius hyperboloid model of hyperbolic geometry. These models represent Riemannian manifolds with positive constant and negative constant curvature respectively. We also derive Gegenbauer expansions for these fundamental solution in geodesic polar coordinates.

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