Standard homogeneous Einstein manifolds and Diophantine equations

Yurii G. Nikonorov; Eugene D. Rodionov

Archivum Mathematicum (1996)

  • Volume: 032, Issue: 2, page 123-136
  • ISSN: 0044-8753

Abstract

top
Some new examples of standard homogeneous Einstein manifolds with semisimple transitive groups of motions and semisimple isotropy subgroups are constructed. For the construction of these examples the solutions of some systems of Diophantine equations are used.

How to cite

top

Nikonorov, Yurii G., and Rodionov, Eugene D.. "Standard homogeneous Einstein manifolds and Diophantine equations." Archivum Mathematicum 032.2 (1996): 123-136. <http://eudml.org/doc/247846>.

@article{Nikonorov1996,
abstract = {Some new examples of standard homogeneous Einstein manifolds with semisimple transitive groups of motions and semisimple isotropy subgroups are constructed. For the construction of these examples the solutions of some systems of Diophantine equations are used.},
author = {Nikonorov, Yurii G., Rodionov, Eugene D.},
journal = {Archivum Mathematicum},
keywords = {Riemannian manifolds; homogeneous spaces; Einstein metrics; homogeneous spaces; Einstein metrics; diophantine equations; classification of solutions},
language = {eng},
number = {2},
pages = {123-136},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Standard homogeneous Einstein manifolds and Diophantine equations},
url = {http://eudml.org/doc/247846},
volume = {032},
year = {1996},
}

TY - JOUR
AU - Nikonorov, Yurii G.
AU - Rodionov, Eugene D.
TI - Standard homogeneous Einstein manifolds and Diophantine equations
JO - Archivum Mathematicum
PY - 1996
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 032
IS - 2
SP - 123
EP - 136
AB - Some new examples of standard homogeneous Einstein manifolds with semisimple transitive groups of motions and semisimple isotropy subgroups are constructed. For the construction of these examples the solutions of some systems of Diophantine equations are used.
LA - eng
KW - Riemannian manifolds; homogeneous spaces; Einstein metrics; homogeneous spaces; Einstein metrics; diophantine equations; classification of solutions
UR - http://eudml.org/doc/247846
ER -

References

top
  1. Cartan É., Geometry of Lie groups and symmetric spaces, IL, Moscow, 1949 (Russian). (1949) 
  2. Manturov O. V., Homogeneous Riemannian manifolds with irreducible isotropy group, Trudy Sem. Vektor. Tensor. Anal. Vyp. 13 (1966), 68-145 (Russian). (1966) MR0210031
  3. Joseph A. Wolf, The geometry and structure of isotropy irreducible homogeneous spaces, Acta Math., 120 (1968), 59-148. (1968) MR0223501
  4. McKenzie Y. W., Ziller W., On normal homogeneous Einstein manifolds, Ann. Sci. Ecole Norm. Sup. (4) 18 (1985), 563-633. (1985) Zbl0598.53049MR0839687
  5. Rodionov E. D., Standard homogeneous Einstein manifolds, Russian Acad. Sci. Dokl. Math. 47 (1993), no.1, 37-40. (1993) Zbl0826.53044MR1216925
  6. Rodionov E. D., Homogeneous Riemannian manifolds with Einstein metrics, Doctor dissertation in Mathematics, Institute of Mathematics, Novosibirsk, 1994. (1994) 
  7. Ireland K., Rosen M., A Classical Introduction to Modern Number Theory, Berlin: Springer-Verlag, 1993. (1993) MR1070716
  8. Dynkin E. B., Semi-simple Subalgebras of Semi-simple Lie Algebras, Transl. Amer. Math. Soc., Series 2, 6 (1957), 111-244. (1957) 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.