A family of helicoidal hypersurfaces, denoted as 𝓧(u, v, s, t), is introduced within the context of the five-dimensional Euclidean space 𝔼⁵. Matrices for the first and second fundamental forms, the ...

Jan 29, 2024 A manifold fitting approach for high-dimensional data reduction beyond Euclidean space (Nanowerk News) National University of Singapore (NUS) statisticians have introduced a new technique ...

"Space still exists with its three dimensions, but it's more like the paint on the canvas rather than the canvas itself." Three-dimensional time is a theory that has been proposed before, though ...

Formally speaking, this means that there must be an algebra monomorphism from the de Rham cohomology of the closed n-manifold to the exterior algebra of the n-dimensional Euclidean space. This ...