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 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 Downloads: Full-text PDF