Lifts of maps to frame bundles

2024/12/27 by Niedzialomski, Kamil, Niedzialomska, Malgorzata
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2412.19891

Abstract

Let (M,g) be a Riemannian manifold, L(M) be its frame bundle, O(M) its orthonormal frame bundle. For a distribution D on M we define a subbundle L(D)⊂ L(M) or O(D)⊂ O(M) in a natural way. This allows us to consider a lift Lφ of a map φ:M→ N not necessarily being a local diffeomorphism. More precisely, if φ:M→ N is a submersion, then Lφ:L(H^φ)→ L(N) or Lφ:O(H^φ)→ L(N), where H^φ is a horizontal distribution of φ. Equipping L(M) and L(N) with the Mok metrics, we study conformality and harmonicity of lifts Lφ.

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