Positive Ricci curvature on simply-connected manifolds with cohomogeneity-two torus actions
نویسندگان
چکیده
منابع مشابه
Positive Ricci Curvature on Highly Connected Manifolds
For k ≥ 2, let M4k−1 be a closed (2k−2)-connected manifold. If k ≡ 1 mod 4 assume further that M is (2k−1)-parallelisable. Then there is a homotopy sphere Σ4k−1 such that M]Σ admits a Ricci positive metric. This follows from a new description of these manifolds as the boundaries of explicit plumbings.
متن کاملHighly connected manifolds with positive Ricci curvature
We prove the existence of Sasakian metrics with positive Ricci curvature on certain highly connected odd dimensional manifolds. In particular, we show that manifolds homeomorphic to the 2k-fold connected sum of S × S admit Sasakian metrics with positive Ricci curvature for all k. Furthermore, a formula for computing the diffeomorphism types is given and tables are presented for dimensions 7 and...
متن کاملOn cohomogeneity one nonsimply connected 7-manifolds of constant positive curvature
In this paper, we give a classification of non simply connected seven dimensional Reimannian manifolds of constant positive curvature which admit irreducible cohomogeneity-one actions. We characterize the acting groups and describe the orbits. The first and second homo-topy groups of the orbits have been presented as well.
متن کاملSimply Connected Manifolds of Positive Scalar Curvature
Hitchin proved that if M is a spin manifold with positive scalar curvature, then the A^O-characteristic number a(M) vanishes. Gromov and Lawson conjectured that for a simply connected spin manifold M of dimension > 5, the vanishing of a(M) is sufficient for the existence of a Riemannian metric on M with positive scalar curvature. We prove this conjecture using techniques from stable homotopy th...
متن کاملon cohomogeneity one nonsimply connected 7-manifolds of constant positive curvature
in this paper, we give a classification of non simply connected seven dimensional reimannian manifolds of constant positive curvature which admit irreducible cohomogeneity-one actions. we characterize the acting groups and describe the orbits. the first and second homo-topy groups of the orbits have been presented as well.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2020
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/14961