We define a new class of manifolds called $n$-Sasakian manifolds that enjoy remarkable geometric properties. We furnish examples of such manifolds and make links to the study of isoparametric hypersurfaces. We demonstrate that these examples carry Einstein metrics.
"$n$-Sasakian manifolds." Tohoku Math. J. (2) 60 (3) 329 - 347, 2008. https://doi.org/10.2748/tmj/1223057731