All supersymmetric degenerate Killing horizons with closed spatial cross sections in D=11 supergravity are either isometric to near-horizon geometries or have vanishing spinorial Lie derivative and are pp-waves when possessing more than 13 supersymmetries.
New quasi-Einstein metrics on a two-sphere
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We construct all axi-symmetric non-gradient $m$-quasi-Einstein structures on a two-sphere. This includes the spatial cross-section of the extreme Kerr black hole horizon corresponding to $m=2$, as well as a family of new regular metrics with $m\neq 2$ given in terms of hypergeometric functions. We also show that in the case $m=-1$ with vanishing cosmological constant the only orientable compact solution in dimension two is the flat torus, which proves that there are no compact surfaces with a metrisable affine connection with skew Ricci tensor.
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UNVERDICTED 2representative citing papers
Proves that a class of quasi-Einstein structures on closed manifolds admit a Killing vector field, extending prior rigidity results and completing classification for compact 2-manifolds while providing new examples.
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Classification of Killing Horizons in D=11 Supergravity
All supersymmetric degenerate Killing horizons with closed spatial cross sections in D=11 supergravity are either isometric to near-horizon geometries or have vanishing spinorial Lie derivative and are pp-waves when possessing more than 13 supersymmetries.
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Quasi-Einstein structures and Hitchin's equations
Proves that a class of quasi-Einstein structures on closed manifolds admit a Killing vector field, extending prior rigidity results and completing classification for compact 2-manifolds while providing new examples.