The length function of geodesic parallel circles. (English) Zbl 0799.53052

Shiohama, K. (ed.), Progress in differential geometry. Tokyo: Kinokuniya Company Ltd.. Adv. Stud. Pure Math. 22, 299-308 (1993).
For an arbitrary simple closed curve \(C\) on an open oriented Riemannian 2-dimensional manifold the authors study the length \(L(t)\) of the geodesic parallel circles of distance \(t>0\) of the curve \(C\). Extending results due to P. Hartmann [Am. J. Math. 86, 705-727 (1964; Zbl 0128.161)] continuity properties of the function \(L\) are given.
For the entire collection see [Zbl 0779.00011].


53C20 Global Riemannian geometry, including pinching


Zbl 0128.161