ON THE STRUCTURE OF CLOSED GENERALIZED EINSTEIN MANIFOLDS AND RIGIDITY PROPERTIES

초록

. In this paper, we show that a closed n-dimensional generalized (lambda, n+ m)-Einstein manifold of constant scalar curvature is isometric to either a sphere n, or a product 1 & times; Sigma n-1 of a circle with an (n - 1)dimensional Einstein manifold of positive Ricci curvature, up to finite cover and rescaling, under the hypothesis that a geometric 2-form vanishes. Furthermore, if we assume (M, g) has positive isotropic curvature, M must be isometric to either a sphere n, or a product 1 & times; n-1 of a circle with an (n - 1)-sphere.

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