Geodesic
Higher order contact of real curves in a real hyperquadric. II
Archivum mathematicum, Tome 34 (1998) no. 3, pp. 361-377 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $P^nV$ 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 $G$.
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 $G$.
Classification : 32F40, 53A55, 53B25, 53B35
Keywords: geometric structures on manifolds; local submanifolds; contacttheory; actions of groups 
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     title = {Higher order contact of real curves in a real hyperquadric. {II}},
     journal = {Archivum mathematicum},
     pages = {361--377},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1998_34_3_a4/}
}
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Villarroel, Yuli. Higher order contact of real curves in a real hyperquadric. II. Archivum mathematicum, Tome 34 (1998) no. 3, pp. 361-377. http://geodesic.mathdoc.fr/item/ARM_1998_34_3_a4/

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