In this paper we introduce and analyze the notion of self-dual k-sets of type (m, n). We show that in a non-square order projective space such sets exist only if the dimension is odd. We prove that, in a projective space of odd dimension r=2s+1(s>=1) and order q, self-dual k-sets of type (m, n), with k ϵ{ϑ2s−q^s,ϑ2s+q^s}, are of elliptic and hyperbolic type, respectively. As a corollary we obtain a new characterization of the non-singular elliptic and hyperbolic quadrics.

Self-dual sets of type (m,n) in projective space

ZANNETTI, MAURO
2004

Abstract

In this paper we introduce and analyze the notion of self-dual k-sets of type (m, n). We show that in a non-square order projective space such sets exist only if the dimension is odd. We prove that, in a projective space of odd dimension r=2s+1(s>=1) and order q, self-dual k-sets of type (m, n), with k ϵ{ϑ2s−q^s,ϑ2s+q^s}, are of elliptic and hyperbolic type, respectively. As a corollary we obtain a new characterization of the non-singular elliptic and hyperbolic quadrics.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/13372
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? ND
social impact