- Main
Sp(2)/U(1) and a positive curvature problem
Published Web Location
https://doi.org/10.1016/j.difgeo.2015.08.002Abstract
A compact Riemannian homogeneous space G/H, with a bi-invariant orthogonal decomposition g=h+m is called positively curved for commuting pairs, if the sectional curvature vanishes for any tangent plane in TeH(G/H) spanned by a linearly independent commuting pair in m. In this paper, we will prove that on the coset space Sp(2)/U(1), in which U(1) corresponds to a short root, admits positively curved metrics for commuting pairs. B. Wilking recently proved that this Sp(2)/U(1) cannot be positively curved in the general sense. This is the first example to distinguish the set of compact coset spaces admitting positively curved metrics, and that for metrics positively curved only for commuting pairs.
Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.
Main Content
Enter the password to open this PDF file:
-
-
-
-
-
-
-
-
-
-
-
-
-
-