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Isometry groups of nearly Kähler manifolds

Mateo Anarella, Michaël Liefsoens

Abstract

Through the means of an alternative and less algebraic method, an explicit expression for the isometry groups of the six-dimensional homogeneous nearly Kähler manifolds is provided.

Isometry groups of nearly Kähler manifolds

Abstract

Through the means of an alternative and less algebraic method, an explicit expression for the isometry groups of the six-dimensional homogeneous nearly Kähler manifolds is provided.

Paper Structure

This paper contains 4 sections, 6 theorems, 40 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The nearly Kähler S³xS³
  3. The nearly Kähler ℂP³
  4. The nearly Kähler flag manifold

Key Result

Theorem 1

The six-dimensional homogeneous nearly Kähler manifolds have the following isometry groups: where $\mathrm{P}(\mathrm{SU}(2)\times\mathrm{SU}(2)\times\mathrm{SU}(2))$ denotes the group $(\mathrm{SU}(2)\times\mathrm{SU}(2)\times\mathrm{SU}(2))/\mathbb{Z}_2$, $S_3$ is the symmetric group of order six, $\mathrm{Sp}(2) = \mathrm{Sp}(4, \mathbb{C}) \cap \mathrm U(4)$ and $\mathrm{PSp}(2) = \mat

Figures (2)

  • Figure 1: The three possible types of lines in $\mathbb{C}P^2$ we can obtain from a flag $(\ell, \pi)$.
  • Figure 2: A representation of all the elements of the fiber, projected onto the plane $\ell^\perp_o$.

Theorems & Definitions (8)

  • Theorem 1
  • Lemma 2
  • Lemma 3
  • Theorem 4
  • proof
  • Theorem 5
  • Theorem 6
  • proof : Proof of Theorem \ref{['theoremisometrygroup']}