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 Surfaces

We show that every compact Einstein Hermitian surface with constant conformal scalar curvature is a Kahler surface and that, in contrast to the compact case, there exits a noncompact Einstein Hermitian and non-Kahler surface with constant conformal scalar curvature.     

On quasi Einstein manifolds

In this paper we give some examples of a quasi Einstein manifold (QE)_n. Next we prove the existence of (QE)_n manifolds. Then we study some properties of a quasi Einstein manifold. Finally the hypersurfaces of a Euclidean space have been studied.     

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.     

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.     

On Hermitian curvature flow on almost complex manifolds

In the present paper we generalize the Hermitian curvature flow introduced and studied in Streets and Tian (2011) [6] to the almost complex case.     

On uniqueness of tangent cones for Einstein manifolds

We show that for any Ricci-flat manifold with Euclidean volume growth the tangent cone at infinity is unique if one tangent cone has a smooth cross-section. Similarly, for any noncollapsing limit of Einstein manifolds with uniformly bounded Einstein constants, we show that local tangent cones are unique if one tangent cone has a smooth cross-section.     

Low-dimensional homogeneous Einstein manifolds

We show that compact, simply connected homogeneous spaces up to dimension admit homogeneous Einstein metrics.

     

On conformally Kähler, Einstein manifolds

We prove that any compact complex surface with admits an Einstein metric which is conformally related to a Kähler metric. The key new ingredient is the existence of such a metric on the blow-up of the complex projective plane at two distinct points.

     

On the renormalized volumes for conformally compact Einstein manifolds

We study the renormalized volume of a conformally compact Einstein manifold. In even dimensions, we derive the analogue of the Chern-Gauss-Bonnet formula incorporating the renormalized volume. When the dimension is odd, we relate the renormalized volume to the conformal primitive of the Q-curvature. __________ Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 17, Differential and Functional Differential Equations. Part 3, 2006.     

Fischer subspaces of Hermitian manifolds

The finite groups generated by 3-transpositions, studied by B.Fischer [5]have a geometrical interpretation given by F.Buekenhout [1] under the name of Fischer spaces.This geometrical concept allows us to study the Fischer subgroups of primitive groups classified by Fischer, and in particular those of unitary groups PSU(n,4), symplectic groups PSp(n,2), orthogonal groups PO(n,2) and symmetric groups Sym(n).This problem is linked to the determination of groups of projectivities generated by clations in characteristic 2 studied by Wagner [9] and McLaughlin[8], and is related to Kantor's work [7] on classical groups generated by long root elements, and to Enright's recent note on Fi₂₂ and Fi₂₃ [5].     

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.