RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
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. Zametki:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Zametki, 2005, Volume 77, Issue 3, Pages 412–423 (Mi mz2502)  

This article is cited in 4 scientific papers (total in 4 papers)

The eigenvalues of the Sinyukov mapping for geodesically equivalent metrics are globally ordered

V. S. Matveev

Chelyabinsk State University

Abstract: Suppose all geodesics of two Riemannian metrics $g$ and $\overline g$ defined on a (connected, geodesically complete) manifold $M^n$ coincide. At each point $x\in M^n$, consider the common eigenvalues $\rho_1,\rho_2,…,\rho_n$ of the two metrics (we assume that $\rho_1\geqslant\rho_2\geqslant…\geqslant\rho_n$)) and the numbers
$$ \lambda_i=(\rho_1\rho_2\dotsb\rho_n)^{1/(n+1)}\frac1{\rho_i}. $$
. We show that the numbers $\lambda_i$ are ordered over the entire manifold: for any two points $x$ and $y$ in M the number $\lambda_k(x)$ is not greater than $\lambda_{k+1}(y)$. If $\lambda_k(x)=\lambda_{k+1}(y)$, then there is a point $z\in M^n$ such that $\lambda_k(z)=\lambda_{k+1}(z)$. If the manifold is closed and all the common eigenvalues of the metrics are pairwise distinct at each point, then the manifold can be covered by the torus.

DOI: https://doi.org/10.4213/mzm2502

Full text: PDF file (236 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2005, 77:3, 380–390

Bibliographic databases:

UDC: 517.9+514.17
Received: 04.02.2000
Revised: 21.04.2003

Citation: V. S. Matveev, “The eigenvalues of the Sinyukov mapping for geodesically equivalent metrics are globally ordered”, Mat. Zametki, 77:3 (2005), 412–423; Math. Notes, 77:3 (2005), 380–390

Citation in format AMSBIB
\Bibitem{Mat05}
\by V.~S.~Matveev
\paper The eigenvalues of the Sinyukov mapping for geodesically equivalent metrics are globally ordered
\jour Mat. Zametki
\yr 2005
\vol 77
\issue 3
\pages 412--423
\mathnet{http://mi.mathnet.ru/mz2502}
\crossref{https://doi.org/10.4213/mzm2502}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2157900}
\zmath{https://zbmath.org/?q=an:1114.53039}
\elib{http://elibrary.ru/item.asp?id=9150081}
\transl
\jour Math. Notes
\yr 2005
\vol 77
\issue 3
\pages 380--390
\crossref{https://doi.org/10.1007/s11006-005-0037-8}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000228965300008}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-20244389396}


Linking options:
  • http://mi.mathnet.ru/eng/mz2502
  • https://doi.org/10.4213/mzm2502
  • http://mi.mathnet.ru/eng/mz/v77/i3/p412

    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

    This publication is cited in the following articles:
    1. Kiosak V., Matveev V.S., “Complete Einstein metrics are geodesically rigid”, Comm. Math. Phys., 289:1 (2009), 383–400  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    2. Kiosak V., Matveev V.S., “Proof of the projective Lichnerowicz conjecture for pseudo-Riemannian metrics with degree of mobility greater than two”, Comm. Math. Phys., 297:2 (2010), 401–426  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    3. Matveev V.S., Rosemann S., “Proof of the Yano-Obata Conjecture for H-Projective Transformations”, J. Differ. Geom., 92:2 (2012), 221–261  crossref  mathscinet  zmath  isi  elib  scopus
    4. Mikes J. Stepanova E. Vanzurova A., “Differential Geometry of Special Mappings”, Differential Geometry of Special Mappings, Palacky Univ, 2015, 1–566  mathscinet  isi
  • Математические заметки Mathematical Notes
    Number of views:
    This page:277
    Full text:116
    References:60
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020