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Jacobi vector fields and the volume of tubes about curves in Sasakian space forms

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We solve explicitly the Jacobi equation on a Sasakian space form and use the solutions to consider explicit formulas for the volume of a geodesic sphere and the volume of a tube about a curve in such a manifold. We obtain some generalizations of H. Weyl's result on the volume of tubes.


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Blair, D.E., Vanhecke, L. Jacobi vector fields and the volume of tubes about curves in Sasakian space forms. Annali di Matematica pura ed applicata 148, 41–49 (1987). https://doi.org/10.1007/BF01774282

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  • Vector Field
  • Explicit Formula
  • Space Form
  • Jacobi Equation
  • Geodesic Sphere