I am reading a paper that uses but does not define the following concept: what is understood by "the Jacobian of the exponential map along a geodesic (beetween two points)"? Is this only defined for geodesics, or for general curves as well? Must the geodesics be length-minimizing?

  • $\begingroup$ The 'Jacobian' usually refers to the first derivative, see en.wikipedia.org/wiki/Jacobian_matrix_and_determinant. Or does it say Jacobi fields? $\endgroup$ – Thomas Feb 18 '15 at 19:26
  • $\begingroup$ Can you also provide the link to your paper? $\endgroup$ – user99914 Feb 18 '15 at 23:43

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