O. Muškarov

Compact self-dual Hermitian surfaces

In this paper, we obtain a classification (up to conformal equivalence) of the compact self-dual Hermitian surfaces. As an application, we prove that every compact Hermitian surface of pointwise constant holomorphic sectional curvature with respect to either the Riemannian or the Hermitian connection is Kahler.

Hermitian structures on Hermitian symmetric spaces

Abstract We show that an inner symmetric space with a compatible Hermitian structure is necessarily Hermitian symmetric, and the Hermitian structure must be invariant. This last result was known for some of the spaces of classical type and was conjectured to be true for all compact Hermitian symmetric spaces in an earlier publication by the first and the last author

Harmonic almost-complex structures on twistor spaces

We prove that the Atiyah-Hitchin-Singer [1] and Eells-Salamon [6] almost-complex structures on the negative twistor space of an oriented Riemannian four-manifold are harmonic in the sense of C. Wood [17, 18] if and only if the base manifold is, respectively, self-dual or self-dual and of constant scalar curvature. The stability of these almost-complex structures is also discussed.

Twistorial Examples of ∗-Einstein Manifolds

In this paper we study the twistor spaces of oriented Riemannianfour-manifolds as a source of almost-Hermitian *-Einstein manifoldsand show that some results in dimension four related to the RiemannianGoldberg–Sachs theorem cannot be extended to higher dimensions.