Bicollared n-manifold in Euclidean space

On images of continuous functions from a compact manifold to Euclidean space

on images of continuous functions from a compact manifold to euclidean space

On the Quaternionic Curves in the Semi-Euclidean Space E_4_2

In this study, we investigate the semi-real quaternionic curves in the semi-Euclidean space E_4_2. Firstly, we introduce algebraic properties of semi-real quaternions. Then, we give some characterizations of semi-real quaternionic involute-evolute curves in the semi-Euclidean space E42 . Finally, we give an example illustrated with Mathematica Programme.

Characterizations of Slant Ruled Surfaces in the Euclidean 3-space

In this study, we give the relationships between the conical curvatures of ruled surfaces generated by the unit vectors of the ruling, central normal and central tangent of a ruled surface in the Euclidean 3-space E^3. We obtain differential equations characterizing slant ruled surfaces and if the reference ruled surface is a slant ruled surface, we give the conditions for the surfaces generate...

Multi-Manifold Modeling in Non-Euclidean spaces

This paper advocates a novel framework for segmenting a dataset on a Riemannian manifold M into clusters lying around lowdimensional submanifolds of M . Important examples of M , for which the proposed algorithm is computationally efficient, include the sphere, the set of positive definite matrices, and the Grassmannian. The proposed algorithm constructs a data-affinity matrix by thoroughly exp...