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Results tagged with riemannian-geometry
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user 5993
Riemannian Geometry is a subfield of Differential Geometry, which specifically studies "Riemannian Manifolds", manifolds with "Riemannian Metrics", which means that they are equipped with continuous inner products.
2
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Let $M$ be a manifold with a conformal structure and a volume measure. How can one reconstru...
A conformal structure with Lorentzian representative produces a conformally invariant causal structure. Causal structure + volume = unique metric is claimed in Bombelli and Meyer (page 2) 1976. I'm un …
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1
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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 …
- 490
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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 …
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