THREE DIMENSIONAL CRITICAL POINT OF THE TOTAL SCALAR CURVATURE

Title & Authors
THREE DIMENSIONAL CRITICAL POINT OF THE TOTAL SCALAR CURVATURE
Hwang, Seungsu;

Abstract
It has been conjectured that, on a compact 3-dimensional orientable manifold, a critical point of the total scalar curvature restricted to the space of constant scalar curvature metrics of unit volume is Einstein. In this paper we prove this conjecture under a condition that ker $\small{s^{\prime}^*_g{\neq}0}$, which generalizes the previous partial results.
Keywords
total scalar curvature;critical point metric;Einstein metric;
Language
English
Cited by
1.
A note on critical point metrics of the total scalar curvature functional, Journal of Mathematical Analysis and Applications, 2015, 424, 2, 1544
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