Bulletin of the
Korean Mathematical Society BKMS

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