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

In the mid-19th century, Bernhard Riemann conceived of a new way to think about mathematical spaces, providing the foundation for modern geometry and physics. Standing in the middle of a field, we can ...

Eugenio Calabi was known to his colleagues as an inventive mathematician — “transformatively original,” as his former student Xiuxiong Chen put it. In 1953, Calabi began to contemplate a class of ...

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.

American Journal of Mathematics, Vol. 131, No. 2 (Apr., 2009), pp. 545-569 (25 pages) Let M be an arbitrary Riemannian manifold diffeomorphic to S². Let x, y be two arbitrary points of M. We prove ...

The field of complex geometry, intertwined with Lie theory, represents a vibrant area where algebraic and differential techniques converge to unravel the structure of complex manifolds and their ...

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 ...