Homogeneous Einstein Finsler Metrics on $(4n+3)$-dimensional Spheres
Canadian mathematical bulletin, Tome 62 (2019) no. 3, pp. 509-523
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In this paper, we study a class of homogeneous Finsler metrics of vanishing $S$-curvature on a $(4n+3)$-dimensional sphere. We find a second order ordinary differential equation that characterizes Einstein metrics with constant Ricci curvature $1$ in this class. Using this equation we show that there are infinitely many homogeneous Einstein metrics on $S^{4n+3}$ of constant Ricci curvature $1$ and vanishing $S$-curvature. They contain the canonical metric on $S^{4n+3}$ of constant sectional curvature $1$ and the Einstein metric of non-constant sectional curvature given by Jensen in 1973.
Huang, Libing; Mo, Xiaohuan. Homogeneous Einstein Finsler Metrics on $(4n+3)$-dimensional Spheres. Canadian mathematical bulletin, Tome 62 (2019) no. 3, pp. 509-523. doi: 10.4153/S0008439518000139
@article{10_4153_S0008439518000139,
author = {Huang, Libing and Mo, Xiaohuan},
title = {Homogeneous {Einstein} {Finsler} {Metrics} on $(4n+3)$-dimensional {Spheres}},
journal = {Canadian mathematical bulletin},
pages = {509--523},
year = {2019},
volume = {62},
number = {3},
doi = {10.4153/S0008439518000139},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439518000139/}
}
TY - JOUR AU - Huang, Libing AU - Mo, Xiaohuan TI - Homogeneous Einstein Finsler Metrics on $(4n+3)$-dimensional Spheres JO - Canadian mathematical bulletin PY - 2019 SP - 509 EP - 523 VL - 62 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4153/S0008439518000139/ DO - 10.4153/S0008439518000139 ID - 10_4153_S0008439518000139 ER -
%0 Journal Article %A Huang, Libing %A Mo, Xiaohuan %T Homogeneous Einstein Finsler Metrics on $(4n+3)$-dimensional Spheres %J Canadian mathematical bulletin %D 2019 %P 509-523 %V 62 %N 3 %U http://geodesic.mathdoc.fr/articles/10.4153/S0008439518000139/ %R 10.4153/S0008439518000139 %F 10_4153_S0008439518000139
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