Examples of minimal G-structures induced by the Lee form

2016/07/26 by Kamil Niedzialomski, Niedzialomski, Kamil
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1607.07777

12 pages

arxiv created 2016/07/26 · arxiv updated 2016/07/27

Abstract

We compute the condition of minimality of a G-structure for the Gray-Hervella class W₄ of almost hermitian manifolds and C₅ class of almost contact metric structures. We also consider C₄ class by comparison with the Grey-Hervella class W₄. The common feature is the existence of the Lee form θ representing these structures. We show that these classes contain minimal G-structures. Here, minimality means minimality of a G-structure inside oriented orthonormal frame bundle SO(M) of a Riemannian manifold M.

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