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A note on constant geodesic curvature curves on surfaces. (English) Zbl 1175.53068
Summary: We are concerned with the structure of curves on surfaces whose geodesic curvature is a large constant. We first discuss the relation between closed curves with large constant geodesic curvature and the critical points of Gauss curvature. Then, we consider the case where a curve with large constant geodesic curvature is immersed in a domain which does not contain any critical point of the Gauss curvature.
MSC:
53C40 Global submanifolds
53C20 Global Riemannian geometry, including pinching
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