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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 …
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 …
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 …