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The existence of a straight line of piecewise Riemannian 2-manifolds


Abstract


In this paper, we study properties of piecewise Riemannian 2-maniflods which are combinatorial 2-manifolds such that each 2-simplex is a geodesic triangle of some Riemannian 2-manifolds. We will introduce the total excess e(X) of a piecewise Riemannian 2-manifold X and prove the following generalizations of results of Cohn-Vossen and the second author obtained for Riemannian 2-manifolds. Let X a piecewise Riemannian 2-manifolds without boundary having one end.

DOI Code: 10.1285/i15900932v18n1p119

Keywords: Piecewise Riemannian manifolds; Total excess; Geodesic

Classification: 53B99; 53C23; 57N05; 53C45; 53C70

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