On open manifolds admitting no complete metric with positive scalar curvature
arxiv(2024)
摘要
In this paper, we investigate the topological obstruction problem for
positive scalar curvature and uniformly positive scalar curvature on open
manifolds. We present a definition for open Schoen-Yau-Schick manifolds and
prove that there is no complete metric with positive scalar curvature on these
manifolds. Similarly, we define weak Schoen-Yau-Shick manifolds by analogy,
which are expected to admit no complete metrics with uniformly positive scalar
curvature.
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