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On a theorem of Ambrose

Part of: Global differential geometry

Published online by Cambridge University Press:  09 April 2009

David J. Wraith
David J. Wraith
Affiliation:
Department of Mathematics, National University of Ireland Maynooth, Ireland, e-mail: dwraith@maths.nuim.ie
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Abstract

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A Riccati inequality involving the Ricci curvature can be used to deduce many interesting results about the geometry and topology of manifolds. In this note we use it to present a short alternative proof to a theorem of Ambrose.

MSC classification

Secondary: 53C20: Global Riemannian geometry, including pinching

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 81 , Issue 2 , October 2006 , pp. 149 - 152
Copyright
Copyright © Australian Mathematical Society 2006

References

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