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13 votes
2 answers
3k views

What's the Lipschitz constant of the exponential map for $\mathrm{SO}(n,R)$?

$\DeclareMathOperator\SO{SO}\DeclareMathOperator\so{\mathfrak{so}}$Consider the Lie algebra $\so(n)$ equipped with the metric $\langle e_i \wedge e_j, e_k \wedge e_l \rangle = \delta_{i,k} \delta_{j,l}...
John Jiang's user avatar
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9 votes
2 answers
715 views

Maximal compact subgroup of $\mathrm{SL}(2,\mathbb{H})$

$\DeclareMathOperator\Spin{Spin}\DeclareMathOperator\Sp{Sp}\DeclareMathOperator\SL{SL}$The exceptional isomorphism $\Spin(5,1)\simeq \SL(2,\mathbb{H})$ is well-known, and I can find references that ...
David Roberts's user avatar
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