Marc Nieper-Wißkirchen

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919 reputation
619
bio website math.uni-augsburg.de/alg
location Augsburg, Germany
age 39
visits member for 4 years, 9 months
seen Apr 28 at 7:19

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?