TY - JOUR
T1 - G-Sasaki Manifolds and K-Energy
AU - Li, Yan
AU - Zhu, Xiaohua
N1 - Publisher Copyright:
© 2019, Mathematica Josephina, Inc.
PY - 2021/2
Y1 - 2021/2
N2 - In this paper, we introduce a class of Sasaki manifolds, called G-Sasaki manifolds with a reductive G-group action on their Kähler cones. By proving the properness of K-energy on such manifolds, we obtain a sufficient and necessary condition for the existence of G-Sasaki–Einstein metrics. A similar result is also obtained for G-Sasaki–Ricci solitons. As an application, we construct many new examples of G-Sasaki–Ricci solitons by an established openness theorem.
AB - In this paper, we introduce a class of Sasaki manifolds, called G-Sasaki manifolds with a reductive G-group action on their Kähler cones. By proving the properness of K-energy on such manifolds, we obtain a sufficient and necessary condition for the existence of G-Sasaki–Einstein metrics. A similar result is also obtained for G-Sasaki–Ricci solitons. As an application, we construct many new examples of G-Sasaki–Ricci solitons by an established openness theorem.
KW - K-energy
KW - Lie group
KW - Sasaki–Einstein metrics
UR - https://www.scopus.com/pages/publications/85074040219
U2 - 10.1007/s12220-019-00285-1
DO - 10.1007/s12220-019-00285-1
M3 - Article
AN - SCOPUS:85074040219
SN - 1050-6926
VL - 31
SP - 1415
EP - 1470
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
IS - 2
ER -