Conjugate radius

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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 M is defined as follows: the injectivity radius at x \in M is the supremum of all values r such that the exponential map from the unit ball B_r(x) in T_xM, to the manifold M, is nonsingular.

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