In the mid-19th century, Bernhard Riemann conceived of a new way to think about mathematical spaces, providing the foundation ...

The Manifold Clock Kickstarter project embraces the mathematical concept of Riemann surfaces to create an artsy 3D timepiece that expresses time through shape and movement. Freelance writer Amanda C.

A mathematical problem solved by Susanna Heikkilä relates to the classification of quasiregularly elliptic 4-manifolds, asking what four-dimensional shapes can be obtained by deforming ...

In this paper, we obtain some classification theorems for totally umbilical semi-invariant sub-manifolds in locally decomposable metallic Riemannian manifolds. We also prove that there exist no ...

As topologists seek to classify shapes, the effort hinges on how to define a manifold and what it means for two of them to be equivalent. Sorting a collection of shapes is child’s play. Circles here, ...

A geodesic in a Riemannian homogeneous manifold (M = G/K, g) is called a homogeneous geodesic if it is an orbit of a one-parameter subgroup of the Lie group G. We investigate G-invariant metrics with ...