Yuri Vyatkin
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 Apr14 revised Curve Orientation on a Surface added 251 characters in body Apr14 answered Curve Orientation on a Surface Apr12 revised How many degrees of freedom are in a flat metric and how does one count them? added 1 character in body Apr12 answered How many degrees of freedom are in a flat metric and how does one count them? Apr12 comment How do I understand constraints on high order derivatives of the Gauss Map? Of course, $T^(i,j)$ is a complete contraction in a sense, but I wanted to say that we take the dot-product of two vectors, whereas the tensors $D^i N$ are not contracted between themselves in the covariant slots. May be, I should have just said that we simply multiply two vectors by the Euclidean dot product in the ambient space, and speaking about "complete contractions" is an overkill. Apr12 comment How do I understand constraints on high order derivatives of the Gauss Map? @Ben I am trying to understand a similar analytical technique but for a hypersurface in an arbitrary Riemannian manifold, an analogue of Taylor theorem, so I am quite interested in this discussion. I have been working in conformal geometry of hypersurfaces for the last few years. It is perhaps too early to announce the results and conjectures publicly, but if you wish we can communicate privately. Apr11 answered How do I understand constraints on high order derivatives of the Gauss Map? Apr10 comment How do I understand constraints on high order derivatives of the Gauss Map? @Ben I added a few additional points to my answer. BTW, could you please uncover somehow, why would you sum these terms? Apr10 revised How do I understand constraints on high order derivatives of the Gauss Map? added 2241 characters in body Apr10 revised How do I understand constraints on high order derivatives of the Gauss Map? Fixed a bad typo Apr10 revised How do I understand constraints on high order derivatives of the Gauss Map? edited body Apr10 answered How do I understand constraints on high order derivatives of the Gauss Map? Mar25 comment Flows of $f$-related vector fields Try to use the uniqueness of solutions of ODEs Mar22 comment LU Factorization - Linear Algebra @RedneckBlueState I think you've done pretty well. Errors is what we all learn from ;-) Mar22 comment LU Factorization - Linear Algebra +1 for being faster that me :-) Mar22 answered LU Factorization - Linear Algebra Mar20 comment Germ induced by a submanifold The submanifold $W$ passes through $p$ and defines the class $W_p$, so $W$ serves as a representative in $W_p$. In other words, this is the usual practice to define an equivalence relation $\sim$ on a set $A$, then pick an element $a \in A$ and refer to the class $[a]$ in $A/\sim$ as to induced by $a$. Of course, $W_p$ depends on $W$ in a sense (more precisely, determined by $W$), and for different $p$-s we get different classes $W_p$. Mar19 comment Germ induced by a submanifold There is a definition of the germ of a submanifold here, which may help. Mar12 comment Deriving Ricci identity for co-vector fields This is a widely used convention to assume that $\nabla$-s act on everything to the right, unless brackets are used. Also, there are pitfalls in this notation. I implicitly use the abstract index notation, which graphically is identical to the usual component notation, but really something like $2 \nabla_{[a} \nabla_{b]} X^c$ means a single tensor, more precisely a tensor field, a section of $T^* M \otimes T^* M \otimes T M$. Mar12 comment Connections and Ricci identity