Geodesic
Higher order contact of real curves in a real hyperquadric
Archivum mathematicum, Tome 32 (1996) no. 1, pp. 57-73.

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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 $G$.
Classification : 32F40, 53B25, 53C15
Keywords: geometric structures on manifolds; local submanifolds; contact theory; actions of groups 
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     author = {Villarroel, Y.},
     title = {Higher order contact of real curves in a real hyperquadric},
     journal = {Archivum mathematicum},
     pages = {57--73},
     publisher = {mathdoc},
     volume = {32},
     number = {1},
     year = {1996},
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     zbl = {0870.53025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1996__32_1_a4/}
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Villarroel, Y. Higher order contact of real curves in a real hyperquadric. Archivum mathematicum, Tome 32 (1996) no. 1, pp. 57-73. http://geodesic.mathdoc.fr/item/ARM_1996__32_1_a4/