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23h
revised Need help understanding a relation between the fundamental forms
Corrected some minor typos and omissions
1d
revised Need help understanding a relation between the fundamental forms
added 2885 characters in body
1d
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
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May
4
revised Dual tensor for partial derivative, if it has any meaning
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May
4
answered Dual tensor for partial derivative, if it has any meaning
Apr
28
revised What is a local invariant?
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Apr
28
answered What is a local invariant?
Apr
28
answered When is the pullback of a tangent bundle along a curve a tangent bundle on the curve?
Apr
28
comment When is the pullback of a tangent bundle along a curve a tangent bundle on the curve?
@Mike There are many various non-isomorphic bundles on a curve, say trivial bundles $I \times \mathbb{R}^k$ of the ranks $k = 1,2,\dots$. In fact, since the segment $I$ is contractible, there are only trivial bundles on $I$. I guess this is what you mean.
Apr
20
comment Induced Connection on $\Sigma\subset M$
The best known to me reference on this topic is B. Andrews, C. Hopper, The Ricci Flow in Riemannian Geometry, see section "1.8 Pullback Bundle Structure" on pp.24-27 with all the proofs. The book is available online on the 1st author's webpage.
Apr
14
revised Curve Orientation on a Surface
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Apr
14
answered Curve Orientation on a Surface
Apr
12
revised How many degrees of freedom are in a flat metric and how does one count them?
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Apr
12
answered How many degrees of freedom are in a flat metric and how does one count them?