# Quasi-positively curved Riemannian manifold

From Diffgeom

*This article defines a property that makes sense for a Riemannian metric over a differential manifold*

*This article defines a property of Riemannian metrics based on the behaviour of the following curvature*: sectional curvature

## Contents

## Definition

A Riemannian manifold is said to have **quasi-positive sectional curvature** or to be **quasi-positively curved** if the following are true:

- The sectional curvature is everywhere nonnegative
- There is a point for which the sectional curvature is strictly positive for all tangent planes