• geometry, the geodesic curvature k g {\displaystyle k_{g}} of a curve γ {\displaystyle \gamma } measures how far the curve is from being a geodesic. For example...
    5 KB (925 words) - 23:29, 22 May 2024
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    the property of having vanishing geodesic curvature. More generally, in the presence of an affine connection, a geodesic is defined to be a curve whose...
    27 KB (3,685 words) - 23:40, 3 May 2024
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    The geodesic curvature at a point is an intrinsic invariant depending only on the metric near the point. A unit speed curve on a surface is a geodesic if...
    128 KB (17,447 words) - 23:59, 27 September 2024
  • Curvature vector and geodesic curvature for appropriate notions of curvature of curves in Riemannian manifolds, of any dimension Degree of curvature Differential...
    44 KB (6,461 words) - 21:09, 16 September 2024
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    manifold with boundary ∂M. Let K be the Gaussian curvature of M, and let kg be the geodesic curvature of ∂M. Then ∫ M K d A + ∫ ∂ M k g d s = 2 π χ ( M...
    13 KB (1,842 words) - 10:54, 1 April 2024
  • A geodesic circle is either "the locus on a surface at a constant geodesic distance from a fixed point" or a curve of constant geodesic curvature. A geodesic...
    1,013 bytes (105 words) - 08:22, 12 May 2024
  • In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Importantly, the world line of a particle free from...
    28 KB (6,157 words) - 02:27, 9 September 2024
  • manifold has non-negative Ricci curvature, then the volume of a geodesic ball is less than or equal to the volume of a geodesic ball of the same radius in...
    34 KB (5,859 words) - 04:51, 6 July 2024
  • Second fundamental form Curvature form Riemann curvature tensor Geodesic curvature Scalar curvature Sectional curvature Ricci curvature, Ricci flat Ricci decomposition...
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    if the curvature of the j {\displaystyle j} th circle is defined as k j = cot ⁡ ρ j , {\textstyle k_{j}=\cot \rho _{j},} the geodesic curvature of the...
    50 KB (6,368 words) - 21:18, 29 July 2024