RT Journal Article
T1 Infinite families of manifolds of positive kth-intermediate Ricci curvature with k small
A1 Domínguez Vázquez, Miguel
A1 González-Álvaro, David
A1 Mouillé, Lawrence
AB Positive kth-intermediate Ricci curvature on a Riemannian n-manifold, to be denoted by Ric_k > 0, is a condition that interpolates between positive sectional and positive Ricci curvature (when k = 1 and k = n − 1 respectively). In this work, we produce many examples of manifolds of Ric_k > 0 with k small by examining symmetric and normal homogeneous spaces, along with certain metric deformations of fat homogeneous bundles. As a consequence, we show that every dimension n ≥ 7 congruent to 3 mod 4 supports infinitely many closed simply connected manifolds of pairwise distinct homotopy type, all of which admit homogeneous metrics of Ric_k > 0 for some k < n/2. We also prove that each dimension n ≥ 4 congruent to 0 or 1 mod 4 supports closed manifolds which carry metrics of Ric_k > 0 with k ≤ n/2, but do not admit metrics of positive sectional curvature.
PB Springer
YR 2023
FD 2023
LK http://hdl.handle.net/10347/35009
UL http://hdl.handle.net/10347/35009
LA eng
NO Domínguez-Vázquez, M., González-Álvaro, D. & Mouillé, L. Infinite families of manifolds of positive kth-intermediate Ricci curvature with k small. Math. Ann. 386, 1979–2014 (2023). https://doi.org/10.1007/s00208-022-02420-w
NO Miguel Domínguez-Vázquez has been supported by projects PID2019-105138GB-C21/AEI/10.13039/501100011033 (Spain), ED431C 2019/10, ED431F 2020/04 (Xunta de Galicia, Spain) and by the Ramón y Cajal program of the Spanish State Research Agency. David González-Álvaro received support from MINECO grant MTM2017-85934-C3-2-P. Lawrence Mouillé was supported in part by NSF Grant DMS-1612049.
DS Minerva
RD 24 abr 2026