• Title, Summary, Keyword: Crofton's formula

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A crofton style formula and its application on the unit sphere $ *$

  • Y. D. Chai;Lee, Young-Soo
    • Bulletin of the Korean Mathematical Society
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    • v.33 no.4
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    • pp.537-544
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    • 1996
  • Crofton's formula on Euclidean plane $E^2$ states: Let $\Gamma$ be a rectifiable curve of length L and let G be a straight line. Then $$ \int_{G \cap \Gamma \neq \phi} n dG = 2L $$ where n is the number of the intersection points of G with the curve $\Gamma$.

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AN INTEGRAL FORMULA AND ITS APPLICATIONS

  • Chai, Y.-D;Kim, Moonjeong
    • Bulletin of the Korean Mathematical Society
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    • v.39 no.1
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    • pp.89-95
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    • 2002
  • In this paper, we obtain an integral formula relating the measure of great spheres $S^{n-2}$ and arc length of a curve on the unit sphere $S^{n-1$ As an application of the formula, we develop a geometric inequality for a spherical curve and prone generalized version of Fenchel's theorem in $S^n$.