An integral formula and its applications
Bull. Korean Math. Soc. 2002 Vol. 39, No. 1, 89-95
Published online March 1, 2002
Y. D. Chai and Moonjeong Kim
Sungkyunkwan University, Sungkyunkwan University
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 prove generalized version of Fenchel's theorem in $R^n$.
Keywords : Crofton's formula, total curvature, pole
MSC numbers : 53C65
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