A Hopf manifold is a quotient of $C^n\backslash 0$ by the cyclic group generated holomorphic contraction. manifolds are diffeomorphic to $S^1\times S^{2n-1}$ and hence do not admit Kahler metrics. It known that defined linear contractions (called manifolds) have locally conformally (LCK) In this paper we prove non-linear embeddings into manifolds, and, moreover they LCK

Algorithms for nonlinear dimensionality reduction (NLDR) find meaningful hidden low-dimensional structures in a high-dimensional space. Current algorithms for NLDR are Isomaps, Local Linear Embedding and Laplacian Eigenmaps. Isomaps are able to reliably recover lowdimensional nonlinear structures in high-dimensional data sets, but suffer from the problem of short-circuiting, which occurs when t...