Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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A NOTE ON DECREASING SCALAR CURVATURE FROM FLAT METRICS

  • Kim, Jongsu (Department of Mathematics, Sogang University)
  • Received : 2013.08.05
  • Accepted : 2013.10.11
  • Published : 2013.12.25
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Abstract

We obtain $C^{\infty}$-continuous paths of explicit Riemannian metrics $g_t$, $0{\leq}t$ < ${\varepsilon}$, whose scalar curvatures $s(g_t)$ decrease, where $g_0$ is a flat metric, i.e. a metric with vanishing curvature. Most of them can exist on tori of dimension ${\geq}3$. Some of them yield scalar curvature decrease on a ball in the Euclidean space.

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References

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