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.[1] A geodesic disk is the region on a surface bounded by a geodesic circle. In contrast with the ordinary circle and disk, the geodesic circle is not necessarily a plane curve and the geodesic disk is not necessarily a planar surface. They can be used to define Gaussian curvature.

References

  1. Whittemore, J. K. (1901). "A Note on Geodesic Circles". The Annals of Mathematics. 3 (1/4): 21–24. doi:10.2307/1967629. ISSN 0003-486X. JSTOR 1967629.


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