Related papers: Remarks on Chern-Einstein Hermitian metrics

In this paper we classify the simply connected, spherical pseudohermitian manifolds whose Webster metric is CR-symmetric.

In a Riemannian manifold, the existence of a new connection is proved. In particular cases, this connection reduces to several symmetric, semi-symmetric and quarter-symmetric connections; even some of them are not introduced so far. We also…

We study the pseudohermitian sectional curvature of a CR manifold.

We give a condition for an almost constant-type manifold to be a constant-type manifold, and holomorphic and $R$-invariant submanifolds of almost Hermitian manifolds are studied. Generalizations of some results in [5] are given.

We report on a few interrelations between bi-Hermitian metrics and locally conformally K\"ahler metrics on complex surfaces.

Domains and more generally complex manifolds whose Bergman metrics have constant holomorphic sectional curvature are characterized. Our approach is to treat the Bergman metrics as the pull-back by the Bergman-Bochner maps of the…

Isotropic almost complex structures induce a class of Riemannian metrics on tangent bundle of a Riemannian manifold. In this paper the curvature tensors of these metrics will be calculated.

We prove that Riemannian metrics with an absolute Ricci curvature bound and a conjugate radius bound can be smoothed to having a sectional curvature bound. Using this we derive a number of results about structures of manifolds with Ricci…

We survey recent results in hermitian integral geometry, i.e. integral geometry on complex vector spaces and complex space forms. We study valuations and curvature measures on complex space forms and describe how the global and local…

We explore complex Riemannian geometry and Hermitian metrics on complex algebraic varieties and analytic spaces, respectively. In particular, we introduce Hermitian metrics on holomorphic Lie algebroids and examine the associated…

In this paper, we investigate the problem of prescribing Chern scalar curvatures on compact Hermitian manifolds with negative Gauduchon degree. By studying the convergence of the associated geometric flow, we obtain some existence results…

We study curvature properties of four-dimensional Lorentzian manifold with two-symmetry property. We then consider Einstein-like metrics, Ricci solitons and homogeneity over these spaces.

Using a semi-symmetric metric connection, we construct Frenet frame and curvatures of curves in 3-dimensional manifolds and give examples of semi-symmetric Frenet curves in Euclidean, Sasakian and Kenmotsu manifolds.

Let L be an ample holomorphic line bundle over a compact complex Hermitian manifold X. Any fixed smooth Hermitian metric on L induces a Hilbert space structure on the space of global holomorphic sections with values in the k:th tensor power…

We give a new variant of $L^2$-extension theorem for the jets of holomorphic sections and discuss the relation between the extension problem of singular Hermitian metrics with semipositive curvature.

This note is about the interplay between the almost-hermitian and Riemannian geometries of a manifold. These geometries can be seen to interact through curvature. The main result is an obstruction equation to the integrability of…

We prove that a simpy connected Hermitian Einstein 4-manifold with non-negative sectional curvature is isometric to complex projective space $\mathbb{C}\mathbb{P}^{2}$ with the Fubini-Study metric or isometric to the product…

The object of the present paper is to study invariant submanifolds of (LCS)n-manifolds with respect to quarter symmetric metric connection. It is shown that the mean curvature of an invariant submanifold of (LCS)n-manifold with respect to…

Warped embeddings from a lower dimensional Einstein manifold into a higher dimensional one are analyzed. Explicit solutions for the embedding metrics are obtained for all cases of codimension 1 embeddings and some of the codimension n>1…

We investigate degenerate special-Hermitian metrics on compact complex manifolds, in particular, degenerate K\"ahler and locally conformally K\"ahler metrics on special classes of non-K\"ahler manifolds.