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 K ̈ahler manifolds. As an application, we prove that a compact flat Riemnannian man- ifold of odd dimension at least 7 cannot be isometrically immersed as a hypersurface of a simply connected, complete Kahler manifold of nonpositive curvature.

Nonflatness of certain contact and CR manifolds. Preprint, submitted.

2014-01-01

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 K ̈ahler manifolds. As an application, we prove that a compact flat Riemnannian man- ifold of odd dimension at least 7 cannot be isometrically immersed as a hypersurface of a simply connected, complete Kahler manifold of nonpositive curvature.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/39196
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