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edited Sep 1, 2015 at 13:03

Given $\xi \in \mathfrak{su}(4)$ and positive $T \in \mathbb{R}$, is it possible to find all smooth curves $U_s \in SU(4)$ with $U_0 = I$ such that

$$\int_0^T U_s \xi U_s^{\dagger} ds =0\; ?$$

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edited Sep 1, 2015 at 2:57

Curves on $SU(4)$ who'swhose adjoint action on $\mathfrak{su}(4)$ integrates to $0$

Given $\xi \in \mathfrak{su}(4)$ and positive $T \in \mathbb{R}$, is it possible to find all curves $U_s \in SU(4)$ with $U_0 = I$ such that:

$\int_0^T U_s \xi U_s^{\dagger} ds =0$$$\int_0^T U_s \xi U_s^{\dagger} ds =0\; ?$$

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asked Sep 1, 2015 at 2:53

Curves on $SU(4)$ who's adjoint action on $\mathfrak{su}(4)$ integrates to $0$

Given $\xi \in \mathfrak{su}(4)$ and positive $T \in \mathbb{R}$, is it possible to find all curves $U_s \in SU(4)$ with $U_0 = I$ such that:

$\int_0^T U_s \xi U_s^{\dagger} ds =0$