Almost complex surfaces in the nearly Kaehler flag manifold

Kamil Cwilinski; Luc Vrancken

Almost complex surfaces in the nearly Kaehler flag manifold

Differential Geometry 2021-07-05 v1

Authors: Kamil Cwilinski , Luc Vrancken

Abstract

We study and classify almost complex totally geodesic submanifolds of the nearly Kaehler flag manifold $F_{1,2}(\mathbb C^3)$ , and of its semi-Riemannian counterpart. We also develop a structural approach to the nearly Kaehler flag manifold $F_{1,2}(\mathbb C^3)$ , expressing for example the curvature tensor in terms of the nearly Kaehler structure $J$ and the three canonical orthogonal complex structures.

Keywords

almost contact manifolds kähler manifolds manifolds

Cite

@article{arxiv.2107.00920,
  title  = {Almost complex surfaces in the nearly Kaehler flag manifold},
  author = {Kamil Cwilinski and Luc Vrancken},
  journal= {arXiv preprint arXiv:2107.00920},
  year   = {2021}
}

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