Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

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.

Stability of total scalar curvature and the critical point equation

Seungsu Hwang, Gabjin Yun

Chung-Ang University; Myongji University

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: 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).