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differential geometry, the cut locus of a point p on a manifold is the closure of the set of all other points on the manifold that are connected to p by...

In Riemannian geometry, an exponential map is a map from a subset of a tangent space TpM of a Riemannian manifold (or pseudo-Riemannian manifold) M to...

allows calculus to be done. A Riemannian metric on a manifold allows distances and angles to be measured. Symplectic manifolds serve as the phase spaces in...

of the definitions given below. Connection Curvature Metric space Riemannian manifold See also: Glossary of general topology Glossary of differential geometry...

mirror parallel to its axis is reflected through the focus. Cut locus (Riemannian manifold) Last geometric statement of Jacobi Nephroid caustic Arnold...

even n), and Yang (odd n). Cut locus (Riemannian manifold) Berger, Marcel (1978). "Blaschke's Conjecture for Sphere". Manifolds all of whose Geodesics are...

no conjugate points. On Riemannian manifolds with non-positive sectional curvature, there are no conjugate points. Cut locus Jacobi field Aurora § Conjugate...

manifold M fixing the common boundary; the quotient space can be identified with N, so that N has a natural orbifold structure. If M is a Riemannian n-manifold...

have equal length. (This is always true of Riemannian globally symmetric spaces of rank 1.) The cut locus of any point p is equal to a hyperplane CPn−1...

Shiing-Shen Chern. His dissertation was entitled "The cut locus and conjugate locus of a Riemannian manifold". Weinstein worked then at MIT on 1967 (as Moore...

coincides with the exponential map of this Riemannian metric. For a general G, there will not exist a Riemannian metric invariant under both left and right...

differentiable on all M. His Ph.D. thesis (1985) transferred the concept of Cut Locus to manifolds with and without boundary. In 1992, essentially a specialisation...

{\displaystyle t=0,\theta =\pi /2} . Now we have a two-dimensional Riemannian manifold with a local radial coordinate chart, g | t = 0 , θ = π / 2 = b (...

(differential geometry), a foliation is an equivalence relation on an n-manifold, the equivalence classes being connected, injectively immersed submanifolds...

differentiable functions. Manifold theory, the study of shapes that are not necessarily embedded in a larger space. Riemannian geometry, the study of distance...

sections of a line bundle locus 1-A subset of projective space given by points satisfying some condition manifold An algebraic manifold is a cycle of projective...

envelope of the cone field. In Riemannian geometry, if a smooth family of geodesics through a point P in a Riemannian manifold has an envelope, then P has...

algebraic geometry Glossary of differential geometry and topology Glossary of Riemannian and metric geometry List of complex and algebraic surfaces List of surfaces...