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- W2281751844 abstract "In this note, we construct new examples of Lorentzian Sasaki-Einstein (LSE) metrics on Smale manifolds $M.$ It has already been established in cite{Gmz2} that such metrics exist on the so-called torsion free Smale manifolds, i.e. the $k$-fold connected sum of $S^{2}times S^{3}.$ Now, we show that LSE metrics exist on Smale manifolds for which $H_{2}(M,mathbb{Z})_{tor}$ is nontrivial. In particular, we show that most simply-connected positive Sasakian rational homology 5-spheres are also negative Sasakian (hence Lorentzian Sasaki-Einstein). Moreover, we show that for each pair of positive integers $(n,s)$ with $n,s >1$, there exists a Lorentzian Sasaki-Einstein Smale manifold $M$ such that $H_{2}(M,{mathbb{Z}})_{tors}=(mathbb{Z}/n)^{2s}$. Finally, we are able to construct so-called mixed Smale manifolds (connect sum of torsion free Smale manifolds with rational homology spheres) which admit LSE metrics and have arbitrary second Betti number. This gives infinitely many examples which do not admit positive Sasakian structures. These results partially address the open problems" @default.
- W2281751844 created "2016-06-24" @default.
- W2281751844 creator A5079562849 @default.
- W2281751844 date "2013-02-14" @default.
- W2281751844 modified "2023-09-27" @default.
- W2281751844 title "A Note on Smale Manifolds and Lorentzian Sasaki-Einstein Geometry" @default.
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- W2281751844 hasPublicationYear "2013" @default.
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