We study Lorentzian affine hypersurfaces of R n+1 having parallel cubic form with respect to the Levi-Civita connection of the affine Berwald-Blaschke metric. As main result, we obtain a complete classification of these hypersurfaces.
Mathematics Subject Classification (2010). Primary 53A15;Secondary 53B25, 53B30.
Abstract. The so-called Cayley hypersurface, constructed by Eastwood and Ezhov, is a higher-dimensional extension of the classical Cayley surface. In this paper, we establish a differential geometric characterization of the Cayley hypersurface, which is an answer to Eastwood and Ezhov's question.
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