Yuri Vyatkin
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 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 May 4 answered Dual tensor for partial derivative, if it has any meaning Apr 28 revised What is a local invariant? added 4 characters in body 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.