Related papers: Kahler manifolds and their relatives

A locally conformally Kaehler (LCK) manifold is a complex manifold admitting a Kaehler covering M, with monodromy acting on M by Kaehler homotheties. A compact LCK manifold is Vaisman if it admits a holomorphic flow acting by non-trivial…

A compact K\"ahler manifold is shown to be simply-connected if its `symmetric cotangent algebra' is trivial. Conjecturally, such a manifold should even be rationally connected. The relative version is also shown: a proper surjective…

In this note, we analyze the question of when will a complex nilmanifold have K\"ahler-like Strominger (also known as Bismut), Chern, or Riemannian connection, in the sense that the curvature of the connection obeys all the symmetries of…

We show that generic rank conditions on the second fundamental form of an isometric immersion $f\colon M^{2n}\to\mathbb{R}^{2n+p}$ of a Kaehler manifold of complex dimension $n\geq 2$ into Euclidean space with low codimension $p$ implies…

Given a compact K\"ahler manifold (X,\omega_0), according to Mabuchi, the set of K\"ahler forms cohomologous to \omega_0 has the natural structure of an infinite dimensional Riemannian manifold. We address the question whether points in…

Motivated by the geometry of Levi degenerate CR hypersurfaces, we define a pre-K\"ahler structure on a complex manifold as a pre-symplectic structure compatible with the almost complex structure, i.e. a closed (1,1)-form. Extending Freeman…

A subbundle of a Hermitian vector bundle $(E, h)$ can be metrically and differentiably defined by the orthogonal projection onto this subbundle. A weakly holomorphic subbundle of a Hermitian holomorphic bundle is, by definition, an…

A locally conformally K\"ahler (lcK) manifold is a complex manifold $(M,J)$ together with a Hermitian metric $g$ which is conformal to a K\"ahler metric in the neighbourhood of each point. In this paper we obtain three classification…

The covariant derivative of the K\"ahler form of an almost pseudo-Hermitian or of an almost para-Hermitian manifold satisfies certain algebraic relations. We show, conversely, that any 3-tensor which satisfies these algebraic relations can…

We show that an indefinite Euclidean complex space is not a relative of an indefinite non-flat complex space form. We further study whether two compact Fubini-Study spaces are relatives or not.

A Riemannian manifold $M$ is called weakly symmetric if any two points in $M$ can be interchanged by an isometry. The compact ones have been well understood, and the main remaining case is that of 2-step nilpotent Lie groups. We give a…

A manifold is locally \emph{$k$-fold symmetric}, if for any point and any $k$-dimensional vector subspace tangent to this point there exists a local isometry such that this point is a fixed point and the differential of the isometry…

In this article, we examine the behavior of the Riemannian and Hermitian curvature tensors of a Hermitian metric, when one of the curvature tensors obeys all the symmetry conditions of the curvature tensor of a K\"ahler metric. We will call…

We call a quaternionic Kaehler manifold with non-zero scalar curvature, whose quaternionic structure is trivialized by a hypercomplex structure, a hyper-Hermitian quaternionic Kaehler manifold. We prove that every locally symmetric…

In this paper we study the homogeneous Kaehler manifolds (h.K.m.) which can be Kaehler immersed into finite or infinite dimensional complex space forms. On one hand we completely classify the h.K.m. which can be Kaehler immersed into a…

We introduce a class of complex manifolds which we call weakly holomorphic homogeneous regular manifolds (wHHR) manifolds. As the name suggests, this class contains the so-called holomorphic homogeneous regular manifolds but also other…

Nearly K\"{a}hler and K\"{a}hler-Codazzi type manifolds are defined in a very similar way. We prove that nearly K\"{a}hler type manifolds have sense just in Hermitian and para-Hermitian contexts, and that K\"{a}hler-Codazzi type manifolds…

We prove two results on geometric consequences of the representation of restricted holonomy group of a Hermitian connection. The first result concerns when such a Hermitian manifold is K\"ahler in terms of the torsion and the irreducibility…

In this paper, we provide a sufficient condition on the non-existence of the common K\"ahler submanifolds between the complex Euclidean space and the ball bundles of some Hermitian vector bundles over K\"ahler manifolds. Then we get the…

Given a compact quantizable pseudo-K\"ahler manifold $(M,\omega)$ of constant signature, there exists a Hermitian line bundle $(L,h)$ over $M$ with curvature $-2\pi i\,\omega$. We shall show that the asymptotic expansion of the Bergman…