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Higher order contact of real curves in a real hyperquadric

PART II

##
*
Yuli Villarroel
*

** Address.**
Departamento de Matematica, Facultad de
Ciencias,
Universidad Central de Venezuela,
Caracas, VENEZUELA

** E-mail:**
yvillarr@euler.ciens.ucv.ve

**Abstract.**
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
\[
Q=\{[\varsigma ]\in P^nV,\;\Phi (\varsigma )=0\}.
\]
\noindent
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 $G$.

**AMSclassification.**
Primary 53C15, Secondary 53B25

**Keywords.**
geometric structures on manifolds, local submanifolds,
contact theory, actions of groups