Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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STABILITY OF TOTAL SCALAR CURVATURE AND THE CRITICAL POINT EQUATION

  • Seungsu Hwang (Department of Mathematics Chung-Ang University) ;
  • Gabjin Yun (Department of Mathematics Myongji University)
  • Received : 2023.02.26
  • Accepted : 2023.07.03
  • Published : 2024.01.31
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Abstract

We consider the total scalar curvature functional, and show that if the second variation in the transverse traceless tensor direction is negative, then the metric is Einstein. We also find the relation between the second variation and the Lichnerowicz Laplacian.

Keywords

Acknowledgement

The authors would like to thank the referee for his/her helpful comments and suggestions. The first-named author was supported by the National Research Foundation of Korea (NRF-2018R1D1A1B05042186) and the second-named author was supported by the National Research Foundation of Korea (NRF- 2019R1A2C1004948). Some parts of this manuscript were written during the second author's stay at the Korea Institute for Advanced Study. He would like to express his gratitude for their hospitality.

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