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Homogeneous Einstein Manifolds with Vanishing
$S$ Curvature
- Part of
- Journal: Canadian Mathematical Bulletin / Volume 62 / Issue 3 / September 2019
- Published online by Cambridge University Press: 22 February 2019, pp. 525-537
- Print publication: September 2019
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View abstract
Infinitely many new Einstein Finsler metrics are constructed on several homogeneous spaces. By imposing certain conditions on the homogeneous spaces, it is shown that the Ricci constant condition becomes an ordinary differential equation. The regular solutions of this equation lead to a two parameter family of Einstein Finsler metrics with vanishing
$S$ curvature.
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Homogeneous Einstein Finsler Metrics on
$(4n+3)$-dimensional Spheres
- Part of
- Journal: Canadian Mathematical Bulletin / Volume 62 / Issue 3 / September 2019
- Published online by Cambridge University Press: 09 November 2018, pp. 509-523
- Print publication: September 2019
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- Article
- Export citation
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View abstract
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.
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