Holonomy restrictions from the curvature operator of the second kind

DOI10.1016/j.difgeo.2023.102010zbMath1525.53060arXiv2208.13820MaRDI QIDQ6044456

Jan Nienhaus, William Wylie, Peter V Petersen, Matthias Wink

Publication date: 19 May 2023

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2208.13820

zbMATH Keywords

holonomylocally symmetric spacesBochner formulascurvature operator of the second kind

Mathematics Subject Classification ID

Differential geometry of symmetric spaces (53C35) Issues of holonomy in differential geometry (53C29) Local Riemannian geometry (53B20)

Related Items (4)

Betti numbers and the curvature operator of the second kind ⋮ Kähler surfaces with six-positive curvature operator of the second kind ⋮ Manifolds with harmonic Weyl tensor and nonnegative curvature operator of the second kind ⋮ Einstein manifolds and curvature operator of the second kind

Cites Work

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• Three-manifolds with positive Ricci curvature
• Manifolds with \(4\frac{1}{2}\)-positive curvature operator of the second kind
• Manifolds with positive curvature operators are space forms
• Symmetric spaces which are real cohomology spheres
• Kähler manifolds and the curvature operator of the second kind
• Sur les groupes d'holonomie homogènes de variétés à connexion affine et des variétés riemanniennes
• Riemannian Geometry
• A Theorem on Holonomy
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