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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 $P^{n}V$ by $$Q=\{\left[\varsigma \right]\in P^{n}V,\Phi \left(\varsigma \right)=0\}.$$ Let $G$ be the subgroup of the special linear group which leaves $Q$ invariant and $D$ the $\left(2n\right)-$ 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...