Riemannian Geometry

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4 domain-specific abstractions whose origin domain is Riemannian Geometry.

• Collapsing manifold — A Riemannian manifold or sequence whose metric geometry approaches a lower-dimensional limit while specified curvature or diameter controls are retained.
• Geodesic convexity — The extension of convex sets and functions to curved spaces by replacing straight line segments with minimizing geodesics.
• Hadamard manifold — A complete, simply connected Riemannian manifold with everywhere nonpositive sectional curvature.
• Isoparametric manifold — Define a Euclidean submanifold with flat normal bundle whose shape operators have constant eigenvalues along every parallel normal field.