J. Aust. Math. Soc. 83 (2007), no. 1, pp. 11–15.

The Monge–Ampère equation and warped products of higher rank

Stefan BechtluftSachs^{†} 
Evangelia Samiou 
Department of Mathematics American University of Beirut P.O. Box 110236 Riad El Solh Beirut 1107 2020 Lebanon sb42.aub.edu.lb 
University of Cyprus Department of Mathematics and Statistics P.O. Box 20537 1678 Nicosia Cyprus samiou@ucy.ac.cy 
Received 8 April 2005; revised 6 May 2006
Communicated by K. Wysocki
Abstract
We show that a warped product M_f=\mathbb {R}^n\times _f\mathbb {R} 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.
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2000 Mathematics Subject Classification:
primary 53C21, 53C24; secondary 35J60

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MathSciNet:
MR2354??? 
Z'blattMATH:
pre05231329 
^{†}indicates author for correspondence 
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