About: Geodesic manifold

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In mathematics, a complete manifold (or geodesically complete manifold) M is a (pseudo-) Riemannian manifold for which, starting at any point p, you can follow a "straight" line indefinitely along any direction. More formally, the exponential map at point p, is defined on TpM, the entire tangent space at p.

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  • In mathematics, a complete manifold (or geodesically complete manifold) M is a (pseudo-) Riemannian manifold for which, starting at any point p, you can follow a "straight" line indefinitely along any direction. More formally, the exponential map at point p, is defined on TpM, the entire tangent space at p. Equivalently, consider a maximal geodesic . Here is an open interval of , and, because geodesics are parameterized with "constant speed", it is uniquely defined up to transversality. Because is maximal, maps the ends of to points of ∂M, and the length of measures the distance between those points. A manifold is geodesically complete if for any such geodesic , we have that . (en)
  • 리만 기하학에서 측지선 완비 준 리만 다양체(測地線完備準Riemann多樣體, 영어: geodesically complete pseudo-Riemannian manifold)는 그 측지선들이 중간에 임의로 끊기지 않는 준 리만 다양체이다. (ko)
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  • 리만 기하학에서 측지선 완비 준 리만 다양체(測地線完備準Riemann多樣體, 영어: geodesically complete pseudo-Riemannian manifold)는 그 측지선들이 중간에 임의로 끊기지 않는 준 리만 다양체이다. (ko)
  • In mathematics, a complete manifold (or geodesically complete manifold) M is a (pseudo-) Riemannian manifold for which, starting at any point p, you can follow a "straight" line indefinitely along any direction. More formally, the exponential map at point p, is defined on TpM, the entire tangent space at p. (en)
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  • Geodesic manifold (en)
  • 측지선 완비 준 리만 다양체 (ko)
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