Hipersuperfícies de Einstein em espaços de produto torcido

Abstract

with n ≥ 2, where I ⊂ R is an open interval, ω is the warping function and Qn ε denotes the simply connected space form of constant sectional curvature ε = −1,0,1. Knowing that constant sectional curvature manifolds (CSC, for short) are the simplest examples of Einstein manifolds, through references such as [5], [7], [11], [13], [14] and [19] we seeked conditions for an Einstein hypersurface of I ×ω Qn ε is necessarily CSC. For certain warping functions ω, we studied the existence of these hypersurfaces through the class of rotational hypersurfaces. Furthermore, using the theory of isoparametric hypersurfaces, we characterized a special type of Einstein hypersurfaces - called ideal - as local graphs of parallel hypersurfaces of Qn ε in which, under certain conditions in main curvatures, are CSC.