Non-negative curvature on certain product manifolds

Fuente: arXiv
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Autor principal: Shen, Wen
Formato: Preprint
Publicado: 2025
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author Shen, Wen
author_facet Shen, Wen
contents Let $G/H$ be a closed, simply connected homogeneous manifold. Suppose every stable class of real vector bundles over $G/H$ contains a homogeneous bundle. Then, for any closed, simply connected smooth manifold $M$ homotopy equivalent to $G/H$, there exists $n>\mathrm{dim}(M)$ such that the product manifold $M\times S^{n}$ admits a metric with non-negative sectional curvature. Many homogeneous manifolds satisfy this assumption, including simply connected compact rank-one symmetric spaces, and among others.
format Preprint
id arxiv_https___arxiv_org_abs_2508_15194
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Non-negative curvature on certain product manifolds
Shen, Wen
Differential Geometry
Geometric Topology
Let $G/H$ be a closed, simply connected homogeneous manifold. Suppose every stable class of real vector bundles over $G/H$ contains a homogeneous bundle. Then, for any closed, simply connected smooth manifold $M$ homotopy equivalent to $G/H$, there exists $n>\mathrm{dim}(M)$ such that the product manifold $M\times S^{n}$ admits a metric with non-negative sectional curvature. Many homogeneous manifolds satisfy this assumption, including simply connected compact rank-one symmetric spaces, and among others.
title Non-negative curvature on certain product manifolds
topic Differential Geometry
Geometric Topology
url https://arxiv.org/abs/2508.15194