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 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 ...

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 ...