The course gives an introduction to smooth manifolds. It covers tangent bundles, vector fields and integral curves (ordinary differential equations), Lie groups, differential forms, and integration.

China’s central bank is making plans to ease restrictions on gold imports, marking a small step toward liberalizing the world’s biggest market for bullion. The People’s Bank of China has released a ...

The Education Department has released a new Nation's Report Card. High school students, especially 12th graders, are reading and learning math and science at historic lows, according to a new report ...

Climate change is creating stronger turbulence. Aircraft designers hope innovative new techniques will reduce its effects. "We saw blood on the ceiling… It was just complete havoc." This was one ...

CRH's Albert Manifold to succeed Helge Lund as BP chairman in October Lund re-elected with reduced support in April Appointment comes as BP navigates major strategy shift Manifold, who has not ...

Nvidia’s latest preview driver has quietly unlocked Smooth Motion support for the RTX 40-series, giving owners of these cards a simple way to boost frame rates in almost any game. Smooth Motion was ...

Abstract: A fundamental issue at the core of trajectory optimization on smooth manifolds is handling the implicit manifold constraint within the dynamics. The conventional approach is to enforce the ...

We continue our previous study of improved Hardy, Rellich and uncertainty principle inequalities on a Riemannian manifold M, started in our earlier paper from 2009. In the present paper we prove new ...

Mathematicians sometimes think of their research as a garden and unsolved problems as seeds waiting to sprout. Some problems are analogous to tulip bulbs. As mathematicians work to solve them, they ...

He came up with an innovative equation called the Ricci flow that helped mathematicians explore fundamental questions that were once out of reach. By Siobhan Roberts Richard Hamilton, an inventive ...

Riemannian manifolds or geodesic metric spaces of finite or infinite dimension occur in many areas of mathematics. We are interested in the interplay between their local geometry and global ...