Geodesic
Invariant Metrics with Nonnegative Curvature on Compact Lie Groups
Canadian mathematical bulletin, Tome 50 (2007) no. 1, pp. 24-34

Voir la notice de l'article provenant de la source Cambridge University Press

We classify the left-invariant metrics with nonnegative sectional curvature on $\text{SO}\left( 3 \right)$ and $U\left( 2 \right)$ .
DOI : 10.4153/CMB-2007-003-7
Mots-clés : 53C20 
Brown, Nathan; Finck, Rachel; Spencer, Matthew; Tapp, Kristopher; Wu, Zhongtao. Invariant Metrics with Nonnegative Curvature on Compact Lie Groups. Canadian mathematical bulletin, Tome 50 (2007) no. 1, pp. 24-34. doi: 10.4153/CMB-2007-003-7
@article{10_4153_CMB_2007_003_7,
     author = {Brown, Nathan and Finck, Rachel and Spencer, Matthew and Tapp, Kristopher and Wu, Zhongtao},
     title = {Invariant {Metrics} with {Nonnegative} {Curvature} on {Compact} {Lie} {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {24--34},
     year = {2007},
     volume = {50},
     number = {1},
     doi = {10.4153/CMB-2007-003-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-003-7/}
}
TY  - JOUR
AU  - Brown, Nathan
AU  - Finck, Rachel
AU  - Spencer, Matthew
AU  - Tapp, Kristopher
AU  - Wu, Zhongtao
TI  - Invariant Metrics with Nonnegative Curvature on Compact Lie Groups
JO  - Canadian mathematical bulletin
PY  - 2007
SP  - 24
EP  - 34
VL  - 50
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-003-7/
DO  - 10.4153/CMB-2007-003-7
ID  - 10_4153_CMB_2007_003_7
ER  - 
%0 Journal Article
%A Brown, Nathan
%A Finck, Rachel
%A Spencer, Matthew
%A Tapp, Kristopher
%A Wu, Zhongtao
%T Invariant Metrics with Nonnegative Curvature on Compact Lie Groups
%J Canadian mathematical bulletin
%D 2007
%P 24-34
%V 50
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-003-7/
%R 10.4153/CMB-2007-003-7
%F 10_4153_CMB_2007_003_7

[1] [1] Cheeger, J., Some examples of manifolds of nonnegative curvature. J. Differential Geometry 8(1973), 623–628. Google Scholar

[2] [2] Cheeger, J. and Gromoll, D., On the structure of complete open manifolds of nonnegative curvature. Ann. of Math. 96(1972), 413–443. Google Scholar

[3] [3] Dickinson, W., Curvature properties of the positively curved Eschenburg spaces. Differential Geom. Appl. 20(2004), no. 1, 101–124. Google Scholar

[4] [4] Eschenburg, J. H., Inhomogeneous spaces of positive curvature. Differential Geom. Appl. 2(1992), no. 1, 123–132. Google Scholar

[5] [5] Geroch, R., Group-quotients with positive sectional curvatures. Proc. Amer.Math. Soc. 66(1977), no. 2, 321–326. Google Scholar

[6] [6] Grove, K. and Ziller, W., Curvature and symmetry of Milnor spheres. Ann. of Math. 152(2000), no. 1, 331–367. Google Scholar

[7] [7] Milnor, J., Curvatures of left-invariant metrics on lie groups. Advances in Math. 21(1976), 293–329. Google Scholar

[8] [8] Püttmann, T., Optimal pinching constants of odd dimensional homogeneous spaces. Ph. D. thesis, Ruhr-Universität, Germany, 1991. Google Scholar

[9] [9] Tapp, K., Quasi-positive curvature on homogeneous bundles. J. Differential Geom. 66(2003), no. 2, 273–287. Google Scholar

[10] [10] Totaro, B., Cheeger manifolds and the classification of biquotients. J. Differential Geom. 61(2002), no. 3, 397–451. Google Scholar

[11] [11] Wallach, N., Compact homogenous Riemannian manifolds with strictly positive curvature. Ann. of Math. 96(1972), 277–295. Google Scholar

[12] [12] Yang, D., On complete metrics of nonnegative curvature on 2-plane bundles. Pacific J. Math. 171(1995), no. 2, 569–583. Google Scholar

Cité par Sources :