# Conjugate radius

From Diffgeom

*This article defines a scalar function on a manifold, viz a function from the manifold to real numbers. The scalar function may be intrinsic or defined in terms of some other structure/functions*

## Definition

The **conjugate radius** is a scalar function on a Riemannian manifold is defined as follows: the injectivity radius at is the supremum of all values such that the exponential map from the unit ball in , to the manifold , is nonsingular.