Abstract：The systole of a closed Riemannian manifold is defined to be the length of a shortest noncontractible loop. Gromov's systolic inequality relates systole to volume, which is a curvature free inequality. Gromov proved that systolic inequality holds on closed essential manifolds. Gromov's further work indicates that systolic inequality is related to topological complicatedness of manifol...
AbstractThere is a large class of Kaluza-Klein type spaces given by the Cartesian product of $1+n$ dimensional Minkowski space with a Ricci-flat Riemannian manifold, called the internal space. These are solutions of the Einstein equation. We will refer to these as SUSY spacetimes. These spaces are stable as solutions of the Einstein equation when $n$ is sufficiently large. The argument uses the...
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