A Riemannian manifold (M, ρ) is called Einstein if the metric ρ satisfies the condition Ric(ρ) = c · ρ for some constant c. This paper is devoted to the investigation of G-invariant Einstein metrics with additional symmetries, on some homogeneous spaces G/H of classical groups. As a consequence, we obtain new invariant Einstein metrics on some Stiefel manifolds SO(n)/SO(l), and on the symplecti...

Joint diagonalization for ICA is often performed on the orthogonal group after a pre-whitening step. Here we assume that we only want to extract a few sources after pre-whitening, and hence work on the Stiefel manifold of p-frames in R. The resulting method does not only use second-order statistics to estimate the dimension reduction and is therefore denoted as soft dimension reduction. We empl...

In this short note, we investigate some features of the space I ( R ,R ) of linear injective maps from R d into R; in particular, we discuss in detail its relationship with the Stiefel manifold Vm,d , viewed, in this context, as the set of orthonormal systems of d vectors in R. Finally, we show that the Stiefel manifold Vm,d is a deformation retract of I ( R ,R ) . One possible application of t...

Abstract We prove that the Stiefel–Whitney classes of a moment-angle manifold, not necessarily smooth, are trivial. also consider partial quotient manifold.