bio | website | math.uni-augsburg.de/alg |
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location | Augsburg, Germany | |
age | 39 | |
visits | member for | 5 years |
seen | 2 days ago | |
stats | profile views | 1,007 |
Jul 2 |
awarded | Curious |
Dec 27 |
accepted | Is the ideal membership problem solvable for differential ideals? Is there a good notion of a Gröbner basis? |
Dec 26 |
comment |
Is the ideal membership problem solvable for differential ideals? Is there a good notion of a Gröbner basis?
The ring $\Omega$ is super-commutative; the generators $x_i$ are of degree $0$, the generators $dx_i$ are of degree $1$. There is just one differential operator, the derivative $d$ of degree $1$, which fulfills $d \circ d = 0$, that is $d(dx_i) = 0$. |
Dec 21 |
asked | Is the ideal membership problem solvable for differential ideals? Is there a good notion of a Gröbner basis? |
Dec 21 |
comment |
Axiomatization of locally compact Hausdorff spaces via compact subspaces
This answer has been helping me most as this gives me more than just rewriting the usual axiom (which is a basic exercise). |
Dec 21 |
accepted | Axiomatization of locally compact Hausdorff spaces via compact subspaces |
Nov 18 |
comment |
What is torsion in differential geometry intuitively?
Your geometric picture is right. |
Nov 16 |
awarded | Yearling |
Nov 6 |
asked | Axiomatization of locally compact Hausdorff spaces via compact subspaces |
Oct 20 |
revised |
Interpetation of torsion and curvature in terms of families of nearby geodesics
added 306 characters in body |
Oct 20 |
comment |
Interpetation of torsion and curvature in terms of families of nearby geodesics
That the geodesics (or the geodesic spray) only encode the affine connection up to torsion, that I know. But I don't think that it means that my question cannot be answered: even in the case of the Jacobi equation, which is on geodesic variation, the torsion enters. This is, of course, because the Jacobi equation talks about the acceleration of the distance between geodesics and the covariant derivative enters in this acceleration directly. I'll edit my question above to make it more clearly. |
Oct 19 |
accepted | Scalar curvature notion for Cartan connections |
Oct 19 |
asked | Interpetation of torsion and curvature in terms of families of nearby geodesics |
Aug 12 |
awarded | Nice Question |
Jul 14 |
awarded | Popular Question |
Jun 25 |
awarded | Promoter |
Apr 27 |
awarded | Notable Question |
Apr 4 |
awarded | Popular Question |
Feb 25 |
comment |
Scalar curvature notion for Cartan connections
@Robert: Please excuse my late silence — I have caught a serious cold and had no head for maths. Will think about your new input during the next days. |
Feb 14 |
comment |
Scalar curvature notion for Cartan connections
Thanks for these thoughts so far; expressing all tensors using the natural coframe makes things much clearer. I have one question, though: In case of $H$ being non-trivial, why would I want to look at $\mathfrak h^* \otimes \Lambda^2 (\mathfrak g/\mathfrak h)$? I specifically do not want to restrict to torsion-free geometries, so I would need something like $\mathfrak g^* \otimes \Lambda^2 (\mathfrak g/\mathfrak h)$, wouldn't I? |