Geodesic Convexity
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics specifically, in Riemannian geometry geodesic convexity is a natural generalization of convexity for sets and functions to Riemannian manifolds. It is common to drop the prefix "geodesic" and refer simply to "convexity" of a set or function. Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.e. with an inner product on the tangent space at each point which varies smo...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics specifically, in Riemannian geometry geodesic convexity is a natural generalization of convexity for sets and functions to Riemannian manifolds. It is common to drop the prefix "geodesic" and refer simply to "convexity" of a set or function. Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.e. with an inner product on the tangent space at each point which varies smoothly from point to point. This gives in particular local notions of angle, length of curves, surface area, and volume. From those some other global quantities can be derived by integrating local contributions.
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