Loading Web-Font TeX/Main/Regular
| Register
\newcommand{\Cat}{{\rm Cat}} \newcommand{\A}{\mathcal A} \newcommand{\freestar}{ \framebox[7pt]{$\star$} }

4. Manifolds of Cohomogeneity-one and Polar Actions


    1. Add remark

      Problem 4.1.

      Study the existence and non-existence of metrics with non-negative curvature on manifolds of cohomogeneity-one.


        • Add remark

          Problem 4.2.

          Find cohomogeneity-one manifolds with “interesting” topology, in particular not homeomorphic to a symmetric space. Study curvature properties of these manifolds.


            • Add remark

              Problem 4.3.

              Classify cohomogeneity-one manifolds with \sec \geq 0 and at least one totally geodesic principal orbit.


                • Add remark

                  Problem 4.4.

                  Compute topological invariants of cohomogeneity-one manifolds. Classify topologically the new candidates for positive curvature.


                    • Add remark

                      Problem 4.5.

                      Study the existence of Einstein metrics on manifolds of cohomogeneity-one.


                        • Add remark

                          Problem 4.6.

                          Suppose M is a polar manifold with \sec > 0. Must M be diffeomorphic to a compact rank-one symmetric space?


                            • Add remark

                              Problem 4.7.

                              Suppose \Sigma \subset M^n is the section of a polar action. If \Sigma is rationally elliptic, must M^n be rationally elliptic?

                                  Cite this as: AimPL: Manifolds with non-negative sectional curvature, available at http://aimpl.org/nnsectcurvature.