# AN INTEGRAL FORMULA AND ITS APPLICATIONS

• Chai, Y.-D (Department of Mathematics, Sungkyunkwan University) ;
• Kim, Moonjeong (Department of Mathematics, Sungkyunkwan University)
• Published : 2002.02.01

#### Abstract

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 $S^n$.

#### References

1. Annales de la Soc. Polonaise v.20 Sur la courbure totale des courbes fermees K. Borsuk
2. Acta. Sci. Math. v.12 Sur certaines inegalties geometriques I. Fary
3. Duke Math. J. v.9 Integral formulas in Crofton's style on the sphere and some inequalities referring to spherical curves L. A. Santalo
4. Hamburger Mathematische Einzelschriften Vorlesungen uber Integralgeometrie W. Blaschke
5. Integral geometry and geometric probability
6. Annals of Math. v.52 On the total curvature of knots J. W. Milnor https://doi.org/10.2307/1969467