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OverviewPlease note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. High Quality Content by WIKIPEDIA articles! In Riemannian geometry, the sphere theorem, also known as the quarter-pinched sphere theorem, strongly restricts the topology of manifolds admitting metrics with a particular curvature bound. The precise statement of the theorem is as follows. If M is a complete, simply-connected, n-dimensional Riemannian manifold with sectional curvature taking values in the interval (1,4] then M is homeomorphic to the n-sphere. (To be precise, we mean the sectional curvature of every tangent 2-plane at each point must lie in (1,4].) Another way of stating the result is that if M is not homeomorphic to the sphere, then it is impossible to put a metric on M with quarter-pinched curvature. Full Product DetailsAuthor: Lambert M. Surhone , Miriam T. Timpledon , Susan F. MarsekenPublisher: VDM Publishing House Imprint: VDM Publishing House Dimensions: Width: 22.90cm , Height: 0.60cm , Length: 15.20cm Weight: 0.171kg ISBN: 9786131192081ISBN 10: 6131192081 Pages: 108 Publication Date: 11 August 2010 Audience: General/trade , General Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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