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geometric structures on manifolds; local submanifolds; contacttheory; actions of groups
Let $\Phi $ be an Hermitian quadratic form, of maximal rank and index $(n,1)$, defined over a complex $(n+1)$ vector space $V$. Consider the real hyperquadric defined in the complex projective space $P^nV$ by \[ Q=\{[\varsigma ]\in P^nV,\;\Phi (\varsigma )=0\}. \] Let $G$ be the subgroup of the special linear group which leaves $ Q $ invariant and $D$ the $(2n)-$ distribution defined by the Cauchy Riemann structure induced over $Q$. We study the real regular curves of constant type in $Q$, tangent to $D$, finding a complete system of analytic invariants for two curves to be locally equivalent under transformations of $G$.
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