All Questions
Tagged with tensor mg.metric-geometry
4 questions
10
votes
2
answers
1k
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Does the hyperdeterminant calculate a quantity akin to the volume of a parallelepiped?
If $M$ is an $n \times n$ matrix, $|\det(M)|$ is the volume of the $n$-dimensional
parallelepiped spanned by the column vectors of $M$.
...
6
votes
1
answer
766
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Does every ‘curvature’ tensor induce a metric? [duplicate]
So we know that given a Riemannian manifold $(M,g)$ we can calculate its Riemannian curvature $R$. This covariant $4$-tensor field then satisfies some important symmetries
\begin{gather*}
R_{ijkl} = - ...
2
votes
1
answer
137
views
Mean Gaussian curvature from non-unit vector
Pg.248 of "Textbook in Tensor Calculus and Differential Geometry" by Prasun Nayak.
Let us suppose that $\lambda_{h|}^i$
is not a unit vector and therefore, the mean curvature $M_h$ in
this ...
1
vote
0
answers
922
views
On a Riemannian manifold, calculate the metric from the distance [closed]
Given a Riemannian manifold $(M,g)$ is it possible to calculate the distance between two points on this manifold. Is it possible the inverse? That means: given a formula of the distance, for example:
...