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Results tagged with semi-riemannian-geometry
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user 121820
Manifolds with a non-degenerate symmetric bilinear form in each tangent space varying differentiably but with constant index and signature.
10
votes
Accepted
Definition of the conformal metric
Let $(M,[g])$ be a conformal manifold;
i.e. $(M,g)$ is a Riemannian manifold and $[g] = \{ u^2g \mathrel{}:\mathrel{} u \in C^\infty(M), u>0 \}$ is the set of Riemannian metrics conformal to $g$.
It i …
- 1,713
2
votes
Accepted
Tensor component calculation
Start by writing
$$ \tag{1}\label{1} B_{nn} = \nabla^\mu \nabla^\nu C_{\mu n n \nu} - \frac{1}{2}C_{\mu n n \nu}R^{\mu\nu} . $$
Here I abuse notation to write $\nabla^\mu\nabla^\nu C_{\mu n n \nu} = n …
- 1,713