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We provide a local classification of selfdual Einstein riemannian four-manifolds admitting a positively oriented hermitian structure and characterize those which carry a hyperhermitian, non-hyperkähler structure compatible with the negative orientation. We show that selfdual Einstein 4-manifolds obtained as quaternionic quotients of $ℍ P^{2}$ and $ℍ H^{2}$ are hermitian.

Self-dual Kähler manifolds and Einstein manifolds of dimension four

Andrzej Derdziński (1983)

Compositio Mathematica

Self-duality of Kähler surfaces

Mitsuhiro Itoh (1984)

Compositio Mathematica

Semilinear equations, the $γ_{k}$ function, and generalized Gauduchon metrics

Jixiang Fu, Zhizhang Wang, Damin Wu (2013)

Journal of the European Mathematical Society

In this paper, we generalize the Gauduchon metrics on a compact complex manifold and define the $γ_{k}$ functions on the space of its hermitian metrics.

Semi-parallel CR submanifolds in a complex space form

Mayuko Kon (2011)

Colloquium Mathematicae

We show that there is no proper CR submanifold with semi-flat normal connection and semi-parallel second fundamental form in a complex space form with non-zero constant holomorphic sectional curvature such that the dimension of the holomorphic tangent space is greater than 2.

Similarity of operators and geometry of eigenvector bundles.

H. K. Kwon, S. Treil (2009)

Publicacions Matemàtiques

Singular Poisson-Kähler geometry of certain adjoint quotients

Johannes Huebschmann (2007)

Banach Center Publications

The Kähler quotient of a complex reductive Lie group relative to the conjugation action carries a complex algebraic stratified Kähler structure which reflects the geometry of the group. For the group SL(n,ℂ), we interpret the resulting singular Poisson-Kähler geometry of the quotient in terms of complex discriminant varieties and variants thereof.

Singularities and Kodaira dimension of the moduli space of flat Hermitian-Yang-Mills connections

Alan Michael Nadel (1988)

Compositio Mathematica

Some critical almost Kähler structures

Takashi Oguro, Kouei Sekigawa (2008)

Colloquium Mathematicae

We consider the set of all almost Kähler structures (g,J) on a 2n-dimensional compact orientable manifold M and study a critical point of the functional $ℱ_{λ, μ} (J, g) = \int_{M} (λ τ + μ τ *) d M_{g}$ with respect to the scalar curvature τ and the *-scalar curvature τ*. We show that an almost Kähler structure (J,g) is a critical point of $ℱ_{- 1, 1}$ if and only if (J,g) is a Kähler structure on M.

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Sasakian manifolds with vanishing contact Bochner curvature tensor and constant scalar curvature

Scalar Curvature and Real Submanifolds of Codimension 2 of a Complex Projective Space.

Scalar-flat Kähler metrics on blown-up ruled surfaces.

Scalar-flat Kähler metrics with SU (2) symmetry.

Scalar-flat Kähler surfaces of all genera.

Sectional curvatures of minimal hypersurfaces immersed in $S^{2 n + 1}$

Selfdual Einstein hermitian four-manifolds

Self-dual Kähler manifolds and Einstein manifolds of dimension four

Self-duality of Kähler surfaces

Semilinear equations, the $γ_{k}$ function, and generalized Gauduchon metrics

Semi-parallel CR submanifolds in a complex space form

Similarity of operators and geometry of eigenvector bundles.

Singular Poisson-Kähler geometry of certain adjoint quotients

Singularities and Kodaira dimension of the moduli space of flat Hermitian-Yang-Mills connections

Some critical almost Kähler structures

Some embeddings of the space of partially complex structures.

Some examples of almost Kähler 4-manifolds.

Some Hermite Metrics in Complex Finsler Spaces

Some Hermite metrics in complex Finsler spaces.

Some Kähler structures on the tangent bundle of a space form.

Currently displaying 1 – 20 of 54