Positively curved cohomogeneity one manifolds and 3-Sasakian geometry
Grove, Karsten ; Wilking, Burkhard ; Ziller, Wolfgang
J. Differential Geom., Tome 78 (2008) no. 1, p. 33-111 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
We provide an exhaustive description of all simply connected positively curved cohomogeneity one manifolds. The description yields a complete classification in all dimensions but 7, where in addition to known examples, our list contains one exceptional space and two infinite families not yet known to carry metrics of positive curvature. The infinite families also carry a 3-Sasakian metric of cohomogeneity one, which is associated to a family of selfdual Einstein orbifold metrics on the 4-sphere constructed by Hitchin.
Publié le : 2008-01-15
Classification:  
@article{1197320603,
     author = {Grove, Karsten and Wilking, Burkhard and Ziller, Wolfgang},
     title = {Positively curved cohomogeneity one manifolds and 3-Sasakian geometry},
     journal = {J. Differential Geom.},
     volume = {78},
     number = {1},
     year = {2008},
     pages = { 33-111},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1197320603}
}

Grove, Karsten; Wilking, Burkhard; Ziller, Wolfgang. Positively curved cohomogeneity one manifolds and 3-Sasakian geometry. J. Differential Geom., Tome 78 (2008) no. 1, pp.  33-111. http://gdmltest.u-ga.fr/item/1197320603/