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Keywords:
geometric structures on manifolds; local submanifolds; contact theory; actions of groups
geometric structures on manifolds; local submanifolds; contact theory; actions of groups
Summary:
Let $\Phi $ be an hermitian quadratic form, of maximal rank and index $(n,1)$% , defined over a complex $(n+1)$ vectorial 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 $(2n-2)$ distribution defined by the Cauchy Riemann structure induced over $Q$. We study the real regular curves of constant type in $Q$, transversal to $D$, finding a complete system of analytic invariants for two curves to be locally equivalent under transformations of $G$.
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