Second, Calabi-Yau manifolds are “Ricci-flat.” According to Albert Einstein’s general theory of relativity, the presence of matter or energy bends space-time, causing so-called Ricci curvature. Calabi ...

If we replace the spheres in curled-up space with these Calabi-Yau shapes, we end up with 10 dimensions: three spatial, plus the six of the Calabi-Yau shapes, plus one of time. If superstring ...

A manifold is a surface or space that can exist in any dimension ... On Christmas Day in 1976, Yau met with Calabi and another mathematician, who confirmed the validity of his proof, establishing the ...

A particle’s mass, the strength of a given force and other fundamental quantities depend on the shape, or geometry, of this convoluted space. String theorists soon made a remarkable discovery. By ...

Wiseman and Headrick (who works at Brandeis University) knew that a Calabi-Yau metric had to solve Einstein’s equations for empty space. A metric satisfying this condition guaranteed that a ...

Gravitational waves are distortions in the fabric of space-time caused by the motion of massive objects ... researchers found that intricate six-dimensional shapes known as Calabi–Yau manifolds ...

But if the universe contains compact, hidden extra dimensions in the shape of Calabi-Yau manifolds ... In one poem, titled “Ode to Space-Time,” Yau writes: So immense our puzzling universe ...

Read the paper: Emergence of Calabi–Yau manifolds in high-precision black ... which measure how ripples in space-time affect the interference of light. Each gravitational signal is a ...

The research reveals the surprising appearance of Calabi-Yau three-fold periods -- complex geometric structures from string theory and algebraic geometry -- within calculations of radiated energy ...