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Mar
21
revised Affine connection, metric and parallel transport and mutual interdependence
Fixed a typo in the main formula
Mar
20
answered Affine connection, metric and parallel transport and mutual interdependence
Mar
13
comment Exterior Derivative vs. Covariant Derivative vs. Lie Derivative
@AlexM. No, I would not say that. As I mentioned in the beginning, connections involve choices (and are abundant). Of course, the naturality of the Levi-Civita connection (which is actually is treated in the reference to (3)) is the best illustration of what I was intending to allude. Another good example would be the naturality of the pullback connection. Giving precise statements was not what I was aiming at in this answer, but I tried to provide references for the curious to dig further.
Mar
4
comment The space of Riemannian metrics on a given manifold.
@AlexM. You have spotted a sloppy point. Thanks for that. I should have said something like "locally like a Fréchet space". For the details please refer to e.g. David G. Ebin, On the space of Riemannian metrics
Feb
14
comment Is every scalar differential operator on $(M,g)$ that commutes with isometries a polynomial of the Laplacian?
Thanks, @Bombyxmori
Feb
14
awarded  Nice Answer
Dec
6
awarded  Good Answer
Sep
20
awarded  Yearling
Jul
28
comment How do I understand constraints on high order derivatives of the Gauss Map?
@Ben I replied to you via e-mail, you can delete the above comment now to avoid spammers.
Jul
8
awarded  Good Answer
May
27
revised Need help understanding a relation between the fundamental forms
Corrected some minor typos and omissions
May
27
revised Need help understanding a relation between the fundamental forms
added 2885 characters in body
May
27
answered Need help understanding a relation between the fundamental forms
May
11
revised Curvature tensors and bivectors
added 2 characters in body
May
11
answered Curvature tensors and bivectors
May
6
comment Index notation.
@bosco yes, this way of using semicolon is just another notation for the covariant derivative: $T_{j k \dots}{}^{l m \dots}{}_{;i} \equiv \nabla_i T_{j k \dots}{}^{l m \dots}$.
May
6
answered Index notation.
May
4
comment Dual tensor for partial derivative, if it has any meaning
@Valery You are welcome. If you mean to strengthen your (multi)linear algebra, Sergei Winitzki, Linear Algebra via Exterior product is highly recommended.
May
4
revised Dual tensor for partial derivative, if it has any meaning
added 11 characters in body
May
4
revised Dual tensor for partial derivative, if it has any meaning
added 12 characters in body