Boundary value problems for the stationary Schrödinger equation on Riemannian manifolds.
Mazepa, E. A. (2002)
Sibirskij Matematicheskij Zhurnal
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Boundary value problems for the stationary Schrödinger equation on Riemannian manifolds.
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The main issue of this paper is an attempt to find a decomposition theorem for infra-nilmanifolds in the same spirit as a result of A. Vasquez for flat Riemannian manifolds. That is: we look for infra-nilmanifolds with prime order holonomy which can be obtained as a fiber space with a non-trivial nilmanifold as fiber and an infra-nilmanifold as its base. In this perspective, we prove the following algebraic result: if E is an almost-Bieberbach group with prime order...
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Let p: M → B be a proper surjective map defined on an (n+2)-manifold such that each point-preimage is a copy of a hopfian n-manifold. Then we show that p is an approximate fibration over some dense open subset O of the mod 2 continuity set C’ and C’ ∖ O is locally finite. As an application, we show that a hopfian n-manifold N is a codimension-2 fibrator if χ(N) ≠ 0 or