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The momentum constraints in the ADM formulation of general relativity

Suppose that the space-time has a time function. Let $g_{ij}$ be the Riemannian metrics of the time slices, and $K_{ij}$ be the second fundamental forms. It is by Codazzi equation that $$ ...
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1answer
93 views

Discrete subgroup of centralizer of transvections in isometries acts properly discontinuously

My question will rely on a clarification of a proof, which I simply don't understand. Let us denote by $X$ a pseudo-riemannian symmetric space and define $$ Z_{\mathrm{Iso}\left(X\right)}G(X) = \{\, ...
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143 views

Diffusion on a semi-Riemannian manifold?

A great deal of literature exists on the heat equation and heat kernel for a Riemannian manifold. The Laplace-Beltrami operator in the given metric replaces the flat Laplacian in the heat equation, ...
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2answers
85 views

Reference request: minimal (maximal) Lorentzian surfaces in $\mathbb{R}^{1,2}$

Let $R^{1,2}$ be the Minkowski 3-space, I would like to know any references about minimal (maximal) orientable Lorentzian surfaces in $\mathbb{R}^{1,2}$, including examples and maybe general theories, ...
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2answers
166 views

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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856 views

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 ...