Einstein metrics on a class of five-dimensional homogeneous spaces

Eugene D. Rodionov

Commentationes Mathematicae Universitatis Carolinae (1991)

  • Volume: 32, Issue: 2, page 389-393
  • ISSN: 0010-2628

Abstract

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We prove that there is exactly one homothety class of invariant Einstein metrics in each space S U ( 2 ) × S U ( 2 ) / S O ( 2 ) r ( r ∈ Q , | r | ≠ 1 ) defined below.

How to cite

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Rodionov, Eugene D.. "Einstein metrics on a class of five-dimensional homogeneous spaces." Commentationes Mathematicae Universitatis Carolinae 32.2 (1991): 389-393. <http://eudml.org/doc/247281>.

@article{Rodionov1991,
abstract = {We prove that there is exactly one homothety class of invariant Einstein metrics in each space $SU(2) \times SU(2) / SO(2)_r (r\in Q, \, |r|\ne 1)$ defined below.},
author = {Rodionov, Eugene D.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {homogeneous Riemannian manifolds; Einstein manifolds; Ricci tensor; sectional curvature; homogeneous Riemannian manifolds; Einstein manifolds; Ricci tensor; sectional curvature},
language = {eng},
number = {2},
pages = {389-393},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Einstein metrics on a class of five-dimensional homogeneous spaces},
url = {http://eudml.org/doc/247281},
volume = {32},
year = {1991},
}

TY - JOUR
AU - Rodionov, Eugene D.
TI - Einstein metrics on a class of five-dimensional homogeneous spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 2
SP - 389
EP - 393
AB - We prove that there is exactly one homothety class of invariant Einstein metrics in each space $SU(2) \times SU(2) / SO(2)_r (r\in Q, \, |r|\ne 1)$ defined below.
LA - eng
KW - homogeneous Riemannian manifolds; Einstein manifolds; Ricci tensor; sectional curvature; homogeneous Riemannian manifolds; Einstein manifolds; Ricci tensor; sectional curvature
UR - http://eudml.org/doc/247281
ER -

References

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  1. Besse A., Einstein manifolds, Springer Verlag, Berlin, 1987. Zbl1147.53001MR0867684
  2. Jensen G.R., Homogeneous Einstein spaces of dimension 4 , J. of Diff. Geom. 3 (1969), 309-349. (1969) MR0261487
  3. Kowalski O., Vanhecke L., Classification of five-dimensional naturally reductive spaces, Math. Proc. Camb. Phil. Soc. 97 (1985), 445-463. (1985) Zbl0555.53024MR0778679

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