On Einstein Hermitian manifolds

We show that every compact Einstein Hermitian surface with constant *–scalar curvature is a K?hler surface. In contrast to the 4-dimensional case, it is shown that there exists a compact Einstein Hermitian (4n + 2)-dimensional manifold with constant *–scalar curvature which is not K?hler. This study is supported by Kangwon National University.     

On Einstein Hermitian manifolds

We show that every compact Einstein Hermitian surface with constant *–scalar curvature is a K?hler surface. In contrast to the 4-dimensional case, it is shown that there exists a compact Einstein Hermitian (4n + 2)-dimensional manifold with constant *–scalar curvature which is not K?hler.     

On CR-submanifolds of Hermitian manifolds

In this paper we consider a CR-submanifold of a Hermitian manifold and prove various integrability theorems on the submanifold. When the ambient space is Kaehlerian a number of differential geometric results are also obtained.     

Dirichlet problem for Hermitian Yang-Mills-Higgs equations over Hermitian manifolds

In this paper, we investigate the Dirichlet problem for one type of vortex equations, which generalize the well-known Hermitian Yang-Mills equations, over general Hermitian manifolds.     

Remarks on Einstein-like Hermitian manifolds

We investigate some relations among Einstein-like conditions on Hermitian manifolds.     

Twistorial examples of almost Hermitian manifolds with Hermitian Ricci tensor

We construct new twistorial examples of non-Kähler almost Hermitian manifolds with Hermitian Ricci tensor by means of a natural almost Hermitian structures on the twistor space of an almost Hermitian four manifold.     

On conformally flat almost Hermitian manifolds

We study some of 2n-dimensional conformally flat almost Hermitian manifolds with J-(anti)-invariant Ricci tensor. Received 13 May 2000; revised 15 February 2001.     

Harmonic maps between compact Hermitian manifolds

In this paper, we generalize the Bochner-Kodaira formulas to the case of Hermitian com- plex (possibly non-holomorphic) vector bundles over compact Hermitian (possibly non-K¨ahler) mani- folds. As applications, we get the complex analyticity of harmonic maps between compact Hermitian manifolds.     

Computing eigenpairs of Hermitian matrices in perfect Krylov subspaces

Numerical Algorithms - For computing the smallest eigenvalue and the corresponding eigenvector of a Hermitian matrix, by introducing a concept of perfect Krylov subspace, we propose a class of...     

Semi-invariant Riemannian maps from almost Hermitian manifolds

We construct Gauss–Weingarten-like formulas and define O’Neill’s tensors for Riemannian maps between Riemannian manifolds. By using these new formulas, we obtain necessary and sufficient conditions for Riemannian maps to be totally geodesic. Then we introduce semi-invariant Riemannian maps from almost Hermitian manifolds to Riemannian manifolds, give examples and investigate the geometry of leaves of the distributions defined by such maps. We also obtain necessary and sufficient conditions for semi-invariant maps to be totally geodesic and find decomposition theorems for the total manifold. Finally, we give a classification result for semi-invariant Riemannian maps with totally umbilical fibers.     

Invariant almost Hermitian structures on flag manifolds

Let G be a complex semi-simple Lie group and form its maximal flag manifold where P is a minimal parabolic (Borel) subgroup, U a compact real form and T=U∩P a maximal torus of U. We study U-invariant almost Hermitian structures on . The (1,2)-symplectic (or quasi-Kähler) structures are naturally related to the affine Weyl groups. A special form for them, involving abelian ideals of a Borel subalgebra, is derived. From the (1,2)-symplectic structures a classification of the whole set of invariant structures is provided showing, in particular, that nearly Kähler invariant structures are Kähler, except in the A₂ case.     

Anti-invariant Riemannian submersions from almost Hermitian manifolds

We introduce anti-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. We give an example, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and check the harmonicity of such submersions. We also find necessary and sufficient conditions for a Langrangian Riemannian submersion, a special anti-invariant Riemannian submersion, to be totally geodesic. Moreover, we obtain decomposition theorems for the total manifold of such submersions.