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searching for Geodesic convexity 3 found (8 total)

Gauss's lemma (Riemannian geometry) (2,176 words) [view diff] exact match in snippet view article

radial isometry, and is of fundamental importance in the study of geodesic convexity and normal coordinates. We define the exponential map at p ∈ M {\displaystyle

Differential geometry of surfaces (17,614 words) [view diff] exact match in snippet view article find links to article

points in it are joined by a unique geodesic. This property is called "geodesic convexity" and the coordinates are called normal coordinates. The explicit calculation

Busemann function (12,928 words) [view diff] exact match in snippet view article find links to article

In geodesic normal coordinates, the metric g(x) = I + ε ‖ x ‖. By geodesic convexity, a geodesic from p to q lies in the ball of radius r = max ‖ p ‖,