About integrability of almost complex structures on strictly Nearly Kähler 6-manifolds
We show that any almost complex structure, positively tamed with $ω$ on nearly Kähler 6-manifold $(M,g,J,ω)$ is not integrable
math.DG↗
arXiv subjects
Natalia Daurtseva
Publications and source records attributed to Natalia Daurtseva.
The space of leftinvariant orthogonal almost complex structures on 6-dimensional Lie groups
The space $\mathcal{Z}$ of leftinvariant orthogonal almost complex structures, keeping the orientation, on 6-dimensional Lie groups is researched. To get explicit view of this space elements the isomorphism of $\mathcal{Z}$ and $\mathbb{C}P^3$ is used. The explicit formula for arbitrary leftinvariant orthogonal almost complex structure on 6-dimensional Lie group as composition of rotations is found.
math.DG↗
Left-invariant almost nearly Kähler structures on $SU(2)\times SU(2)$ in the tetrahedron visualization for $CP^3$
The set of maximal non-integrable structures $(SU(2)\times SU(2),B,I)$, where $B$ is Killing-Cartan metric is described as subset of $\mathbb{CP}^3$. The visualization of complex projective space $\mathbb{CP}^3$ as tetrahedron which edges and faces are $\mathbb{CP}^1$ and $\mathbb{CP}^2$ is used.
math.DG↗