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The Monge-Ampère equation and warped products of higher rank

Published online by Cambridge University Press:  09 April 2009

Stefan Bechtluft-Sachs
Affiliation:
Department of MathematicsAmerican University of BeirutP.O. Box 11-0236 Riad El Solh Beirut 1107 2020Lebanonsb42.aub.edu.lb
Evangelia Samiou
Affiliation:
University of CyprusDepartment of Mathematics and Statistics P.O. Box 20537 1678 Nicosia [email protected]
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Abstract

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We show that a warped product Mf = nf has higher rank and nonpositive curvature if and only if f is a convex solution of the Monge-Ampère equation. In this case we show that M contains a Euclidean factor.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2007

References

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