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RICCI AND SCALAR CURVATURES ON SU(3)
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  • Journal title : Honam Mathematical Journal
  • Volume 34, Issue 2,  2012, pp.231-239
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2012.34.2.231
 Title & Authors
RICCI AND SCALAR CURVATURES ON SU(3)
Kim, Hyun-Woong; Pyo, Yong-Soo; Shin, Hyun-Ju;
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 Abstract
In this paper, we obtain the Ricci curvature and the scalar curvature on SU(3) with some left invariant Riemannian metric. And then we get a necessary and sufficient condition for the scalar curvature (resp. the Ricci curvature) on the Riemannian manifold SU(3) to be positive.
 Keywords
Ricci curvature;scalar curvature;Einstein manifold;
 Language
English
 Cited by
1.
HARMONIC HOMOMORPHISMS BETWEEN TWO LIE GROUPS, Honam Mathematical Journal, 2016, 38, 1, 1  crossref(new windwow)
 References
1.
S. Aloff and N. R. Wallach, An infinite family of distinct 7-manifolds admitting positively Riemannian metrics, Bull. Amer. Math. Soc. 81 (1975), 93-97. crossref(new window)

2.
A. L. Besse, Einstein Manifolds, Springer Verlag (1987).

3.
S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. 1, 1963

4.
S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. 2, 1969, John Wiley and Sons, New York.

5.
M. Kreck and S. Stolz, Some nondiffeomorphic homogeneous 7-manifolds with positive sectional curvature, J. Differential Geom. 33 (1991), 465-486.

6.
K. Nomizu, Invariant affine connections on homogeneous spaces, Amer. J. Math. 76 (1954), 33-65. crossref(new window)

7.
J.-S. Park, Stability of the identity map of SU(3)=T (k, l), Tokyo J. Math. 17(2) (1994), 281-289. crossref(new window)

8.
J.-S. Park, Curvatures on SU(3)=T (k, l), to appear in Kyushu J. Math., 2012.

9.
J.-S. Park, Y.-S. Pyo and Y.-L. Shin, Weyl structures on compact connected Lie groups, J. Chungcheong Math. Soc. 24(3) (2011), 503-515.

10.
Y.-S. Pyo, Y.-L. Shin and J.-S. Park, Yang-Mills connections on Closed Lie groups, Honam Math. J. 32(4) (2010), 651-661. crossref(new window)

11.
H. Urakawa, Numerical computation of the spectra of the Laplacian on 7- dimensional homogeneous manifolds $SU(3)=T_{k,l}$, SIAM J. Math. Anal. 15 (1984), 979-987. crossref(new window)

12.
H. Urakawa, The first eigenvalue of the Laplacian for a positively curved homogeneous Riemannian manifold, Compositio Math. 59 (1986), 57-71.

13.
N. Wallach, Harmonic Analysis on Homogeneous Spaces, Dekker, New York, 1973.

14.
M. Y. Wang, Some examples of homogeneous Einstein manifolds in dimension seven, Duke Math. J. 49 (1982), 23-28. crossref(new window)