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Some special solutions of the Einstein-Maxwell action with a non-negative cosmological constant and a very heavy point mass particle have been obtained. The solutions correspond to static spacetime of locally constant curvature in its spatial part and a constant magnetic field of a magnetic monopole together with deficit of angle at the location of point mass. The quantum mechanics of a point particle in these spacetimes in the absence of angular deficit has been solved algebraically both relativistically and non-relativistically. It has been also shown that these 2-dimensional Hamiltonians have the degeneracy group of GL(2,c) type and para-supersymmetry of arbitrary order or shape invariance, which is originated from a SO(4,c) group.
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