On the geometry of spheres in L-spaces

It is shown that any two points on the surface of the unit ball ofL ¹(μ), where the measureμ is non-atomic, may be joined in the surface by a curve whose length is equal to the straight-line distance between its endpoints. This property is contrasted with the metric properties of the unit sphere in other L-spaces. This work was supported in part by NSF grant GP-19126.