Higher order contact of real curves in a real hyperquadric


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