Classification of Locally Euclidean Spaces

Locally Peripherally Euclidean Spaces Are Locally Euclidean, Ii.

A Characterization of Locally Euclidean Spaces

Phone classification in pseudo-euclidean vector spaces

Recently we have proposed a structural framework for modelling speech, which is based on patterns of phonological distinctive features, a linguistically well-motivated alternative to standard vector-space acoustic models like HMMs. This framework gives considerable representational freedom by working with features that have explicit linguistic interpretation, but at the expense of the ability t...

On the Classification of Quadratic Harmonic Morphisms between Euclidean Spaces

We give a classification of quadratic harmonic morphisms between Euclidean spaces (Theorem 2.4) after proving a Rank Lemma. We also find a correspondence between umbilical (Definition 2.7) quadratic harmonic morphisms and Clifford systems. In the case R −→ R, we determine all quadratic harmonic morphisms and show that, up to a constant factor, they are all bi-equivalent (Definition 3.2) to the ...

Classification of Spherical Lagrangian Submanifolds in Complex Euclidean Spaces

An isometric immersion f : Mn → M̃n from a Riemannian nmanifold Mn into a Kähler n-manifold M̃n is called Lagrangian if the complex structure J of the ambient manifold M̃n interchanges each tangent space of Mn with the corresponding normal space. In this paper, we completely classify spherical Lagrangian submanifolds in complex Euclidean spaces. In this paper, we also provide two corresponding cla...