Rigidez e topologia de variedades quase-Einstein com fronteira

Abstract

In this work, we study the compact ( ; n + m)􀀀Einstein manifolds with boundary, where m 1: Based in [10], we provide topological characterizations for the boundary and as consequence of a Bochner type formula, we provide a gap result for compact space-time perfect static uid with positive constant scalar curvature. In sequel, from [12], we extend for the class of generalized ( ; n+m)􀀀Einstein manifold, some classical results about compact static manifolds wth boundary, namely, due to Chrúsciel [11] and Boucher, Gibbons and Horowitz [5] . Finally, from [9], we provide some rigidity results for ( ; n + m)􀀀Einstein manifolds under some conditions on Bach tensor.