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 
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