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Examples of Minimal \(\varvec{G}\)-structures

  • Kamil Niedziałomski
Open Access
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Abstract

Let M be an oriented Riemannian manifold and SO(M) its oriented orthonormal frame bundle. Assume there exists a reduction \(P\subset SO(M)\) of the structure group \(SO(\dim M)\) to a subgroup G. We say that a G-structure M is minimal if P is a minimal submanifold of SO(M), where we equip SO(M) in the natural Riemannian metric. We give non-trivial examples of minimal G-structures for \(G=U(\dim M/2)\) and \(G=U((\dim M-1)/2)\times 1\) having some special features—locally conformally Kähler and \(\alpha \)-Kenmotsu manifolds, respectively.

Keywords

G-structure intrinsic torsion minimal submanifold locally conformally Kähler manifold \(\alpha \)-Kenmotsu manifold 

Mathematics Subject Classification

53C10 53C25 53C43 

Notes

Acknowledgements

I wish to thank anonymous referee for many suggestions that led to improvement of the paper.

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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of ŁódźLodzPoland

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