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Manifolds with a non-degenerate symmetric bilinear form in each tangent space varying differentiably but with constant index and signature.

2 votes

Eikonal equation and double null coordinates

Per Willie's answer, locally this is the same thing. The global situation is, predictably, very different. I don't know anything specifically about the eikonal equation, but I do know about global sol …
Ben Whale's user avatar
  • 490
1 vote

Usage/Application of Raychaudhuri equation in Riemann geometry or pure maths

The Raychaudhuri Equation is called the Raychaudhuri Equation because of a physist called Raychaudhuri. In mathematics the same equation occurs, for the reason you have pointed out, but it is called s …
Ben Whale's user avatar
  • 490
1 vote

Lower bound for domain of exponential map on Lorentzian manifolds

You've waited a long time for an answer. And I am surprised that no one has written one. Let $M=\mathbb{R}\times(0,\infty)$. The exponential map isn't defined at $(x,t)$ for vectors $(u,s)$ with $s<-t …
Ben Whale's user avatar
  • 490