Bull. Korean Math. Soc. 2024; 61(1): 281-290
Online first article January 22, 2024 Printed January 31, 2024
https://doi.org/10.4134/BKMS.b230111
Copyright © The Korean Mathematical Society.
Seungsu Hwang, Gabjin Yun
Chung-Ang University; Myongji University
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: Stability of the curvature functional, the total scalar curvature, Einstein
MSC numbers: Primary 53C25; Secondary 58E11
Supported by: 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).
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