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Results tagged with semi-riemannian-geometry
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user 40549
Manifolds with a non-degenerate symmetric bilinear form in each tangent space varying differentiably but with constant index and signature.
7
votes
Properties that only Lorentzian manifolds have
The reverse Cauchy-Schwarz inequality: for any two causal vectors (orientation in this `squared' formulation is not relevant) $v, w$ we have
$$
\vert g(v,w)\vert^2\ge g(v,v) g(w,w)
$$
is false in pseu …
3
votes
Usage/Application of Raychaudhuri equation in Riemann geometry or pure maths
The Bochner identity is a special case of the Raychaudhuri equation, obtained when the vector field is of gradient type.
Let $v$ be a vector field and let $a^\alpha=v^\alpha{}_{;\beta} v^\beta$ be its …
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