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On the Geodesic Curvature of Riemannian Loops

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Abstract

We give a sharp extrinsic lower bound for the total geodesic curvature of a closed curve in a space form and discuss the equality case. The case of curves in Euclidean 3-space which is known since a long time by means of integral geometry, is extended here in a new way.

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Authors and Affiliations

  1. Département de Mathématiques, Université d’Evry-Val d’Essonne, Boulevard des Coquibus, 91025, Evry Cedex, France

    Alain R. Veeravalli

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  1. Alain R. Veeravalli
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Correspondence to Alain R. Veeravalli.

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Dedicated to Elljee and Lucas Zakaria.

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Veeravalli, A.R. On the Geodesic Curvature of Riemannian Loops. Results. Math. 39, 353–356 (2001). https://doi.org/10.1007/BF03322695

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  • DOI: https://doi.org/10.1007/BF03322695

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