Abstract
The relationship between curvature and topology has traditionally been one of the most popular and highly developed topics in Riemannian geometry. In this area, a central issue of concern is that of determining global topological structures from local metric properties. Of particular interest to us the so- called pinching problem and related sphere theorems in geometry. We begin with a brief overview of this problem, from Hopf’s inspiration to the latest developments in Hamilton’s Ricci flow.
Keywords
- Riemannian Manifold
- Sectional Curvature
- Compact Riemannian Manifold
- Ricci Flow
- Constant Sectional Curvature
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© 2011 Springer-Verlag Berlin Heidelberg
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Andrews, B., Hopper, C. (2011). Introduction. In: The Ricci Flow in Riemannian Geometry. Lecture Notes in Mathematics(), vol 2011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16286-2_1
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DOI: https://doi.org/10.1007/978-3-642-16286-2_1
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16285-5
Online ISBN: 978-3-642-16286-2
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