Bechtluft-Sachs, Stefan; Samiou, Evangelia The Monge-Ampère equation and warped products of higher rank. (English) Zbl 1133.53030 J. Aust. Math. Soc. 83, No. 1, 11-15 (2007). Summary: 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 an Euclidean factor. MSC: 53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions 53C24 Rigidity results 35J60 Nonlinear elliptic equations PDFBibTeX XMLCite \textit{S. Bechtluft-Sachs} and \textit{E. Samiou}, J. Aust. Math. Soc. 83, No. 1, 11--15 (2007; Zbl 1133.53030) Full Text: DOI References: [1] Kowalski, J. Math. Pures Appl. 71 pp 471– (1992) [2] Gutiérrez, Progr. in Nonlinear Differential Equations Appl. (2001) [3] DOI: 10.1007/BF02698934 · Zbl 0643.53037 · doi:10.1007/BF02698934 [4] DOI: 10.2307/1971331 · Zbl 0585.53031 · doi:10.2307/1971331 [5] Bemdt, Osaka J. Math. 39 pp 383– (2002) [6] DOI: 10.2307/1971303 · Zbl 0598.53046 · doi:10.2307/1971303 [7] DOI: 10.2307/1971373 · Zbl 0589.53047 · doi:10.2307/1971373 [8] Boeckx, Riemannian Manifolds of conullity two (1996) · Zbl 0904.53006 · doi:10.1142/3198 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.