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monica
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Torsion-free $G$-Structures
awarded
 Scholar
accepted
$SU(n)$-invariant subring of $\Lambda^{*}\mathbb{R}^{2n}$
asked
$SU(n)$-invariant subring of $\Lambda^{*}\mathbb{R}^{2n}$
awarded
 Student
comment
Torsion-free $G$-Structures
what do you mean by "parallel transport of these $\omega_{i}$ will act as a $P$-transformation on the $\omega_{i}$"? Why does this hold?
comment
Torsion-free $G$-Structures
the above splitting you mentioned is orthogonal in $SO(n)$ with respect to what metric? Bi-invariant metric in $SO(n)$ ?
comment
Torsion-free $G$-Structures
you consider the connection 1-forms as a matrix (locally) $(\omega_{ij})$. Why does its value split into a part of the Lie Algebra of $G$ and one into the Orthogonal complement of the Lie Algebra of $G$ inside $SO(n)$? Why does it make sense to define the torsion like this (as the orthogonal complement)?
asked
Torsion-free $G$-Structures