On the geometry of orthonormal frame bundles. II

DOI10.1007/s10455-007-9091-7zbMath1141.53023OpenAlexW2056698413WikidataQ125680266 ScholiaQ125680266MaRDI QIDQ927171

Masami Sekizawa, Oldřich Kowalski

Publication date: 4 June 2008

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10455-007-9091-7

zbMATH Keywords

Riemannian manifoldscalar curvatureRicci curvatureEinstein spacehomogeneous spaceorthonormal frame bundle

Mathematics Subject Classification ID

Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07) Global submanifolds (53C40) Global Riemannian geometry, including pinching (53C20) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (2)

Curvatures of the diagonal lift from an affine manifold to the linear frame bundle ⋮ On the frame bundle adapted to a submanifold

Cites Work

• Lifts of tensor fields to the frame bundle
• On the curvature of the induced Riemannian metric on the frame bundle of a Riemannian manifold
• Three- and four-dimensional Einstein-like manifolds and homogeneity
• Einstein metrics on principal fibre bundles
• The fundamental equations of a submersion
• On the geometry of orthonormal frame bundles
• On the differential geometry of frame bundles of Riemannian manifolds.
• Naturally reductive metrics and Einstein metrics on compact Lie groups
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