A class of Riemannian manifolds that pinch when evolved by Ricci flow |
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Authors: | M Simon |
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Institution: | Universit?t Freiburg, Eckerstra?e 1, 79104 Freiburg, Germany.?E-mail: msimon@bingo.mathematik.uni-freiburg.de, DE
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Abstract: | The purpose of this paper is to construct a set of Riemannian metrics on a manifold X with the property that will develop a pinching singularity in finite time when evolved by Ricci flow. More specifically, let , where N
n
is an arbitrary closed manifold of dimension n≥ 2 which admits an Einstein metric of positive curvature. We construct a (non-empty) set of warped product metrics on the non-compact manifold X such that if , then a smooth solution , t∈0,T) to the Ricci flow equation exists for some maximal constant T, 0<T<∞, with initial value , and
where K is some compact set .
Received: 8 March 1999 |
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Keywords: | Mathematics Subject Classification (1991):53C20 53C21 53C25 53C44 |
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