Some Aspects of Theory of Schrödinger Operators on Riemannian Manifold

Farah Diyab; B. Surender Reddy

doi:10.26713/cma.v13i5.2258

Authors

Farah Diyab Department of Mathematics, Osmania University, Hyderabad, India https://orcid.org/0000-0001-5564-2519 (unauthenticated)
B. Surender Reddy Department of Mathematics, Osmania University, Hyderabad, India https://orcid.org/0000-0002-6078-9934 (unauthenticated)

DOI:

https://doi.org/10.26713/cma.v13i5.2258

Keywords:

Manifolds, Spectral theory, Laplacian, Spectral geometry

Abstract

This paper deals with a given Riemannian manifold \(\mathcal{M}\). One of the main tasks is description of spectrum of several classes of Schrödinger operator \(P=\frac{-h^{2}}{2}\Delta _{g}+V\) where \(\Delta _{g}\) is Laplace Beltrami operator and \(V\) is potential on manifold. We illustrate the inverse and direct problems of \(\Delta _{g}\) and the way to discover the geometry of Riemannian manifold from spectral data.

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