On the differential geometry of frame bundles of Riemannian manifolds.

DOI10.1515/crll.1978.302.16zbMath0378.53016OpenAlexW1599935046WikidataQ115236844 ScholiaQ115236844MaRDI QIDQ4157644

Kam-Ping Mok

Publication date: 1978

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://www.digizeitschriften.de/dms/resolveppn/?PPN=GDZPPN002195232

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Global Riemannian geometry, including pinching (53C20) Fiber bundles in algebraic topology (55R10)

Related Items (27)

Modelling anisotropic covariance using stochastic development and sub-Riemannian frame bundle geometry ⋮ Prolongation of G-structures to the frame bundle ⋮ Metrics and connections on the bundle of affinor frames ⋮ Natural transformations of symmetric affine connections on manifolds to metrics on linear frame bundles: A classification ⋮ Geodesics of Sasakian metrics on tensor bundles ⋮ Isometry groups of Riemannian fibrations ⋮ Curvatures of the diagonal lift from an affine manifold to the linear frame bundle ⋮ On the geometry of orthonormal frame bundles. II ⋮ Geometry of tangent bundles and spaces over algebras ⋮ Groups of transformations of Riemannian manifolds ⋮ On the geometry of orthonormal frame bundles ⋮ Martingales on frame bundles ⋮ Tangent and frame bundle harmonic lifts ⋮ Some properties of Sasakian metrics in cotangent bundles ⋮ Differential geometry and stochastic dynamics with deep learning numerics ⋮ The frame bundle picture of Gaussian wave packet dynamics in semiclassical mechanics ⋮ Lifts of tensor fields to the frame bundle ⋮ On the geometry of the \((1,1)\)-tensor bundle with Sasaki type metric ⋮ Odd-dimensional orbifolds with all geodesics closed are covered by manifolds ⋮ An infinitesimal probabilistic model for principal component analysis of manifold valued data ⋮ On the frame bundle adapted to a submanifold ⋮ Generalization of Selberg's 3/16 theorem for convex cocompact thin subgroups of \(\operatorname{SO}(n, 1)\) ⋮ Unimodular measures on the space of all Riemannian manifolds ⋮ Exponential mixing of frame flows for convex cocompact hyperbolic manifolds ⋮ Connections on differentiable fiber bundles ⋮ Almost complex structure in the frame bundle of an almost contact metric manifold ⋮ Motions and homotheties in Finsler spaces and their generalizations

This page was built for publication: On the differential geometry of frame bundles of Riemannian manifolds.