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Results tagged with tensor
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user 85934
2
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$1$-parameter family of metrics preserving the normal direction
Let $(M^n,g)$ be a compact Riemannian manifold with boundary, $n \geq 2$, and let $N$ be the unit outward normal to $\partial M$. Denote by $S^2(M)$ the symmetric covariant $2$-tensors, by $S^2_0(M)$ …
- 2,095
5
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How is this product of tensors defined?
eigenvalue of a small geodesic ball in a riemannian manifold”, by Karp and Pinsky, from where I took the following:
Here, $\Delta_{-2}$ denotes the usual Laplacian in $\mathbb{R}^n$, $R$ is the curvature tensor … of the manifold and $\rho$ is defined by
$$ \rho(x) = \sum_{i,j} \rho_{ij} x_i x_j$$
where $\rho_{ij}$ are the components of the Ricci tensor of the manifold. …
- 2,095