Hipersuperfícies do R4 invariantes por um subgrupo de isometrias com curvatura escalar nula

Abstract

In this dissertation we study hypersurfaces with zero scalar curvature. The work is based on hypersurfaces that are invariant by an isometry subgroup and are generated by curves parametrized by arc length. These curves are used to transform the partial dierential equations S, given by local coordinates, into ordinary dierential equations given by the coordinates of the curves that generate the hypersurfaces. We made a summary of the qualitative study of ordinary dierential equations to conclude the dissertation, analyzing the dierential equations and classifying the O (3)-invariant hypersurfaces and O(2) x O(2)-invariant hypersurfaces with zero scalar curvature.