RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Sb., 2000, Volume 191, Number 7, Pages 73–88 (Mi msb492)  

On differential-geometric characteristics of Veronese curves

V. V. Konnov

Moscow State Pedagogical University

Abstract: One part of the algebraizability problem for smooth submanifolds of a projective space is to find differential-geometric invariants of concrete algebraic varieties. In this paper, a property characterizing the Veronese curves $W^1_n$ is discovered and proved. A necessary and sufficient condition for a pair of smooth curves to lie on one Veronese curve is also found. Let $\gamma\times\gamma\setminus\operatorname{diag}(\gamma\times \gamma)$ be the manifold parametrizing pairs of distinct points on a curve $\gamma$, and let $\gamma _1\times \gamma _2$ be the manifold parametrizing pairs of points on two curves $\gamma_1$ and $\gamma_2$ embedded in a projective space $P^n$. A system of differential invariants $J_1,J_2,…,J_{n-1}$, is constructed on the manifolds $\gamma\times \gamma\setminus\operatorname{diag}(\gamma\times\gamma )$ and $\gamma_1\times \gamma_2$. These invariants have the following geometric interpretation. On the manifold $\gamma\times\gamma\setminus\operatorname{diag}(\gamma\times\gamma)$ the condition $J_1\equiv J_2\equiv…\equiv J_{n-1}\equiv1$ means that $\gamma$ is a Veronese curve $W^1_n$. On the manifold $\gamma_1\times\gamma_2$ the condition $J_1\equiv J_2\equiv…\equiv J_{n-1}\equiv1$ is equivalent to the fact that the curves $\gamma_1$ and $\gamma_2$ lie in one Veronese curve $W^1_n$.

DOI: https://doi.org/10.4213/sm492

Full text: PDF file (292 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2000, 191:7, 1015–1031

Bibliographic databases:

UDC: 514.76
MSC: Primary 53A20, 14H45; Secondary 53C10
Received: 22.02.1999

Citation: V. V. Konnov, “On differential-geometric characteristics of Veronese curves”, Mat. Sb., 191:7 (2000), 73–88; Sb. Math., 191:7 (2000), 1015–1031

Citation in format AMSBIB
\Bibitem{Kon00}
\by V.~V.~Konnov
\paper On differential-geometric characteristics of Veronese curves
\jour Mat. Sb.
\yr 2000
\vol 191
\issue 7
\pages 73--88
\mathnet{http://mi.mathnet.ru/msb492}
\crossref{https://doi.org/10.4213/sm492}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1809929}
\zmath{https://zbmath.org/?q=an:1011.53009}
\transl
\jour Sb. Math.
\yr 2000
\vol 191
\issue 7
\pages 1015--1031
\crossref{https://doi.org/10.1070/sm2000v191n07ABEH000492}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000165473200004}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0034341508}


Linking options:
  • http://mi.mathnet.ru/eng/msb492
  • https://doi.org/10.4213/sm492
  • http://mi.mathnet.ru/eng/msb/v191/i7/p73

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:391
    Full text:75
    References:21
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019