Six-Dimensional Nearly Kähler Manifolds of Cohomogeneity One (II)

By F. Podestà, A. Spiro. Communications in Mathematical Physics, 2009

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Let M be a six dimensional manifold, endowed with a cohomogeneity one action of G = SU2 × SU2, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{\rm reg} \subset M}$$\end{document} its subset of regular points. We show that Mreg admits a smooth, 2-parameter family of G-invariant, non-isometric strict nearly Kähler structures and that a 1-parameter subfamily of such structures smoothly extends over a singular orbit of type S3. This determines a new class of examples of nearly Kähler structures on T S3.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/403affe0585d5bfe9e7dd57ce8d46ebbd7a37ac1

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In Applied Mathematics

1. Lorenzo Foscolo
2. M. Haskins
3. M. Li
4. Iskander A. Taimanov
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In Geometry and Topology

1. Lorenzo Foscolo
2. M. Haskins
3. M. Li
4. Iskander A. Taimanov
5. Dmitry Berdinsky

Citations in the corpus

• New G$_2$-holonomy cones and exotic nearly Kähler structures on $S^6$ and $S^3 \times S^3$ (2017, background): “: hypo and nearly hypo structures respectively. For applications to the construction of complete compact cohomogeneity one nearly Kahler 6{manifolds it follows from the results of Podesta and Spiro [40] (recalled in more detail at the beginning of Section 3) that the only interesting case is that of”