Some Aspects of Theory of Schrödinger Operators on Riemannian Manifold - Diyab, Farah; Reddy, B. Surender (Communications in Mathematics and Applications, 2022)
This paper deals with a given Riemannian manifold \(M\). One of the main tasks is description of spectrum of several classes of Schrödinger operator \(P=-h^2 2Δ _g+V\) where \(Δ _g\) is Laplace Beltrami operator and \(V\) is potential on manifold. We illustrate the inverse and direct problems of \(Δ _g\) and the way to discover the geometry of Riemannian manifold from spectral data.