User Wombat

Wombat

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Trying to make a burrow ...

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Two definitions of linearly independent vector fields

Jul 16, 2021

Linearization of scalar curvature: $DR|_g(h)=-\Delta_g(\mathrm{tr}_g h)+\mathrm{div}_g(\mathrm{div}_g h)-\langle\mathrm{Ric}_g,h\rangle_g$

Nov 15, 2022

Do orthogonal projections play a role in diagonalizability?

Jul 30, 2020

Piecewise smooth vector field along a one-parameter family of curves

Aug 31, 2021

Is the "Its transpose is its inverse" definition of an orthogonal matrix equivalent to the "It preserves the dot product" definition?

Jul 12, 2021

Proof of the Meyers–Serrin theorem (the "$H=W$" theorem)

Sep 22, 2022

How do we get $\frac{\partial}{\partial t}|_{t=0}(h_t)_{ij}=\langle\nabla_{e_i}X,e_j\rangle+\langle e_i,\nabla_{e_j}X\rangle$?

May 15

How do I work with a connection in $TM$ when the inputs are vector fields defined ONLY on an open subset of $M$?

Aug 19, 2021

Why does the Levi-Civita connection on a flat manifold satisfy the flatness criterion?

Sep 6, 2021

The smallest $\sigma$-algebra in $X=\{1,2,3,4\}$ that contains a collection of subsets of $X$

Dec 23, 2021