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

The Monge–Ampère equation and warped products of higher rank

Stefan Bechtluft-Sachs Evangelia Samiou
Department of Mathematics
American University of Beirut
P.O. Box 11-0236
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
(Metadata: XML, RSS, BibTeX) MathSciNet: MR2354??? Z'blatt-MATH: pre05231329
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