On the geodesic flow of surfaces of nonpositive curvature
classification
🧮 math.DS
keywords
flatcurvaturenonpositiveprovesurfacebiggerboundedclasses
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Let $S$ be a surface of nonpositive curvature of genus bigger than 1 (i.e. not the torus). We prove that any flat strip in the surface is in fact a flat cylinder. Moreover we prove that the number of homotopy classes of such flat cylinders is bounded.
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