The geometry of spacetime forms the very foundation of modern gravitational theory, where the elegant interplay between curvature and matter is described by Einstein’s field equations. In this ...

Riemannian geometry provides the essential framework for analysing curved spaces by endowing manifolds with a smoothly varying metric. This field has enabled statisticians to extend classical ...

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 ...

Proceedings of the American Mathematical Society, Vol. 139, No. 12 (DECEMBER 2011), pp. 4475-4486 (12 pages) Let M⁴ be a PL-manifold of nonnegative curvature that is homeomorphic to a product of two ...