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.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.