Hopf Rinow Theorem
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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, the Hopf Rinow theorem is a set of statements about the geodesic completeness of Riemannian manifolds. It is named after Heinz Hopf and his student Willi Rinow (1907 1979).Furthermore, any one of the above implies that given any two points p and q in M, there exists a length minimizing geodesic connecting these two points (geodesics are in general extrema, and may or may not be minima). This does not hold in infinite dimensions: (Atkin 1975) showed…mehr

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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, the Hopf Rinow theorem is a set of statements about the geodesic completeness of Riemannian manifolds. It is named after Heinz Hopf and his student Willi Rinow (1907 1979).Furthermore, any one of the above implies that given any two points p and q in M, there exists a length minimizing geodesic connecting these two points (geodesics are in general extrema, and may or may not be minima). This does not hold in infinite dimensions: (Atkin 1975) showed that two points in an infinite dimensional complete Riemannian manifold need not be connected by any geodesic.