Subvariedades de tipo espaço com curvatura escalar constante em espaços-forma semi-Riemannianos

Abstract

In this work, we obtain some results about spacelike submanifolds with constant scalar curvature in semi-Riemannian space forms, using a Simons type formula and a differential operator introduced by Cheng-Yau. In order to achieve this we impose some conditions either on the length of the second fundamental form, or on the sectional curvatures or for the mean curvature vector. The results for complete (non-compact) and compact submanifolds were obtained separately.