The Diameter and the Mean Distance of a Riemannian Manifold
نویسنده
چکیده
Let M be a compact Riemannian manifold. For x, y G M, denote by p(x,y) the distance between x and y, i.e., the infimum of lengths of continuous piecewise C paths between x and y. (Notice that for geodesically complete manifolds there is always a path from x to y of length p(x,y).) The invariants of M based on the distance p are called metrical invariants. Most of them are related to the geometry of M. Let us mention a few of them. The diameter, diam(M), of M is the maximal value of p(x, y) for x,y e M. If two points x, y are at distance diam(M), they are called antipodal. Denote by
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