arXiv subjects
Publications and source records attributed to N. A. Daurtseva.
The nearly Kähler structures on the 6-sphere, as a twistor bundle sections are researched. We show that for any point of twistor bundle there exists an 1-parametric family of sections, passing through the point, which give nearly Kähler structures on the round sphere. Some properties of those sections are found.
There exist non-degenerate 3-form $dω_I$, $ω_I(X,Y)=g(IX,Y)$, for each leftinvariant almost Hermitian structure $(g,I)$, where $g$ is Killing-Cartan metric on the $M=S^3\times S^3=SU(2)\times SU(2)$. Known \cite{H1}, that arbitrary non-degenerate 3-form on the 6-dimensional manifold, with some additional properties defines the almost complex structure. Condition for $I$ to define almost complex structure $J_I$ by $dω_I$ is obtained. Properties of $J_I$ are researched.
Invariant complex structures on the homogeneous manifold $U(n+1)/U(n)\times U(p+1)/U(p)$ are reseached. The critical point of the functional of the scalar curvature is found.
Invariant complex structures on the homogeneous manifold $U(n+1)/U(n)\times U(p+1)/U(p)$ are reseached. Extreme values of sectional curvature of Hermitian metrics on this manifold are found.
The space ${\mathcal A}$ of almost complex structures on a closed manifold $M$ is studied. A natural parametrization of the space ${\mathcal A}$ is defined. It is shown, that ${\mathcal A}$ is a infinite dimensional complex weak Pseudo-Riemannian manifold. A curvature of the space ${\mathcal A}$ is found. The space ${\mathcal A}_ω$ of associated almost complex structures on a symplectic manifold $M,ω$ and space ${\mathcal AO}$ of orthogonal almost complex structures on a Riemannian manifold $M,g_0$ are considered in more detail.