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 ...

A mathematical problem solved by Susanna Heikkilä relates to the classification of quasiregularly elliptic 4-manifolds, ...

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 ...

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 ...

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 ...