Date of Award
Doctor of Philosophy (PhD)
We study the topology of closed, simply-connected, 6-dimensional Riemannian
manifolds of positive sectional curvature which admit isometric actions by SU(2) or
SO(3). We show that their Euler characteristic agrees with that of the known exam-
ples, i.e. S6, CP3, the Wallach space SU(3)=T 2 and the biquotient SU(3)==T 2. We
also classify, up to equivariant dieomorphism, certain actions without exceptional
orbits and show that there are strong restrictions on the exceptional strata.
Liu, Yuhang, "On Closed Six-Manifolds Admitting Metrics With Positive Sectional Curvature And Non-Abelian Symmetry" (2019). Publicly Accessible Penn Dissertations. 3388.