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EnglishIn 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.
| Titolo: | Self-dual sets of type (m,n) in projective space |
| Autori: | |
| Data di pubblicazione: | 2004 |
| Rivista: | |
| 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. |
| Handle: | http://hdl.handle.net/11697/13372 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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