Deformation of the -curvature

作者：Santos Almir Silva^*; Andrade Maria

来源：Annals of Global Analysis and Geometry, 2018, 54(1): 71-85.

DOI：10.1007/s10455-018-9593-5

• sigma(2)-Curvature
• sigma(2)-Singular space
• Flat metrics
• Rigidity result
• Almost-Schur-type lemma

Our main goal in this work is to deal with results concern to the -curvature. First we find a symmetric 2-tensor canonically associated to the -curvature and we present an almost-Schur-type lemma. Using this tensor, we introduce the notion of -singular space and under a certain hypothesis we prove a rigidity result. Also we deal with the relations between flat metrics and -curvature. With a suitable condition on the -curvature, we show that a metric has to be flat if it is close to a flat metric. We conclude this paper by proving that the three-dimensional torus does not admit a metric with constant scalar curvature and nonnegative -curvature unless it is flat.

• 出版日期2018-7