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Computing the Frenet-Serret trihedron in $\Bbb L^3$ (Lorentz-Minkowski space)

Consider $\Bbb L^3 = (\Bbb R^3, \langle , \rangle)$, with the convention $$\langle (x_1,y_1,z_1), (x_2,y_2,z_2)\rangle = x_1x_2+y_1y_2 - z_1z_2$$ and $\| v \| = \sqrt{|\langle v, v \rangle|}$. Let ...
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Are all orbits semi-Riemannian submanifolds?

Let $M$ be a semi-Riemannian manifold and $G\subset Iso(M)$ a closed connected Lie subgroup which acts properly on $M$. It is known that every orbit of the action is a (closed) submanifold of $M$. My ...
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Hodge decomposition in Minkowski space

This question is motivated by the physical description of magnetic monopoles. I will give the motivation, but you can also jump to the last section. Let us recall Maxwell’s equations: Given a ...