Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1894632 | Journal of Geometry and Physics | 2015 | 5 Pages |
Abstract
We prove that, under a suitable geometric condition, a Riemannian manifold of dimension at least 7 endowed with a contact distribution cannot be flat. This result yields nonflatness of some classes of almost contact metric manifolds, contact sub-Riemannian symmetric spaces, locally symmetric CR spaces and CR submanifolds of Kähler manifolds. As an application, we prove that a compact flat Riemannian manifold of odd dimension at least 7 cannot be isometrically immersed as a hypersurface of a simply connected, complete Kähler manifold of nonpositive curvature.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
A. Lotta,