Abstract
Let M be a complete Riemannian manifold with sectional curvature KM>-H>0, Bonnet's theorem tells us that the fundamental group π1(M) of M is finite. In this note, we'll determine π1(M) under some conditions on the closed geodesics in M.
Keywords
- Riemannian Manifold
- Fundamental Group
- Sectional Curvature
- Closed Geodesic
- Complete Riemannian Manifold
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References
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W. Klingenberg, Riemannian Geometry. Walter de Gruyter. Berlin New York. 1982.
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© 1987 Springer-Verlag
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Xia, C.Y. (1987). Remarks on the fundamental group of positively curved manifolds. In: Gu, C., Berger, M., Bryant, R.L. (eds) Differential Geometry and Differential Equations. Lecture Notes in Mathematics, vol 1255. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077690
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DOI: https://doi.org/10.1007/BFb0077690
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-17849-1
Online ISBN: 978-3-540-47883-6
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