Abstract
Let M be a Riemannian manifold. A complete geodesic γ on M means that γ:(-∞,+∞)→M is a normalized geodesic. In this paper, we prove that on (S 2,g) with positive curvature, any two complete geodesics must intersect an infinite number of times, and a complete geodesic must self-intersect an infinite number of times.
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Mathematics Subject Classification (2000)
53C40 (53C22)
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Zhou, D. The intersection of complete geodesics on S 2 with positive curvature. Ann. Mat. Pura Appl. IV. Ser. 182, 315–324 (2003). https://doi.org/10.1007/s10231-002-0069-6
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DOI: https://doi.org/10.1007/s10231-002-0069-6