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Results tagged with dg.differential-geometry
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user 156792
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
5
votes
2
answers
531
views
Bounds for metric in normal coordinate
Let $M$ be a Riemannian $n$-manifold and $x \in M$. For the metric tensor $g_{ij}$ of geodesic normal coordinates at $x$, there is a formula $g_{ij}(y) = \delta_{ij} + \frac13 R_{kijl} y^k y^l + O(\|y …
- 4,123
7
votes
1
answer
307
views
Fundamental domain for two Grassmannians
Let $\pi_1, \pi_2$ be two $k$-dimensional subspaces of $\mathbb R^n$. Using elements of the orthogonal group $O(n)$, how much can we simplify $\pi_1, \pi_2$? Certainly there always exists $A \in O(n)$ …
- 903
3
votes
0
answers
426
views
Taylor's theorem for embedded manifolds
For an embedded Riemannian manifold $M \subseteq \mathbb{R}^m$ and a point $x \in M$, there is a series expansion (page 8 of Monera's paper):
$$\exp_x(t v) = x + t J_x(v) + \frac{t^2}{2!} Q_x(v) + \c …
- 903