Related papers: Bi-Hermitian gray surfaces II

The aim of this paper is to give examples of compact neutral 4-manifolds $(M,g)$ whose Ricci tensor $\rho$ satisfies the relation $\nabla_X\rho(X,X) =\frac13X\tau g(X,X)$. We present also a family of new Einstein bi-Hermitian neutral…

We consider biconservative surfaces $\left(M^2,g\right)$ in a space form $N^3(c)$, with mean curvature function $f$ satisfying $f>0$ and $\nabla f\neq 0$ at any point, and determine a certain Riemannian metric $g_r$ on $M$ such that…

We prove several K\"ahlerness criteria for compact Hermitian surfaces under semi-definiteness assumptions on natural Ricci curvatures of the Strominger-Bismut connection. The key tools for proving these results are explicit identities…

Given a Hermitian manifold $(M^n,g)$, the Gauduchon connections are the one parameter family of Hermitian connections joining the Chern connection and the Bismut connection. We will call $\nabla^s = (1-\frac{s}{2})\nabla^c +…

The aim of this work is to give a twistor presentation of recent results about bi-Hermitian metrics on compact complex surfaces with odd first Betti number.

In this paper, we establish Chern number identities on compact complex surfaces. As an application, we prove that if $(M,g)$ is a compact Riemannian four-manifold with constant scalar curvature and admits a compatible complex structure $J$…

Let X and X' be compact Riemann surfaces of genus at least three. Let G and G' be nontrivial connected semisimple linear algebraic groups over C. If some components $M_{DH}^d(X,G)$ and $M_{DH}^{d'}(X',G')$ of the associated Deligne--Hitchin…

In this paper, we show that, for a biharmonic hypersurface $(M,g)$ of a Riemannian manifold $(N,h)$ of non-positive Ricci curvature, if $\int_M|H|^2 v_g<\infty$, where $H$ is the mean curvature of $(M,g)$ in $(N,h)$, then $(M,g)$ is minimal…

We investigate bi-Hermitian metrics on compact complex surfaces with odd first Betti number producing new examples with connected anti-canonical divisor using the general construction of \cite{abd15}. The result is a complete classification…

We compactify M(atrix) theory on Riemann surfaces Sigma with genus g>1. Following [1], we construct a projective unitary representation of pi_1(Sigma) realized on L^2(H), with H the upper half-plane. As a first step we introduce a suitably…

We give a classification of compact conformally Kahler Einstein-Weyl manifolds whose Ricci tensor is hermitian.

Let $M^2_{g,k}$ and $M^2_{g',k'}$ be compact Riemann surfaces with punctures ($g,g'\ge 0$ - genuses, $k,k'\ge 1$ - number of punctures). For any Hausdorff space $X$ the quotient space $\mathrm{Sym}^nX := X^n/S_n$ is the $n$-th symmetric…

We consider rigidity properties of compact symmetric spaces $X$ with metric $g_0$ of rank one. Suppose $g$ is another Riemannian metric on $X$ with sectional curvature $\kappa$ bounded by $0 \leq \kappa \leq 1$. If $g$ equals $g_0$ outside…

The aim of this paper is to classify three dimensional compact Riemannian manifolds $(M^{3},g)$ that admits a non-constant solution to the equation $$-\Delta f g+Hess f-fRic=\mu Ric+\lambda g,$$ for some special constants $(\mu, \lambda)$,…

I show that any complex manifold that resembles a rank two compact Hermitian symmetric space (other than a quadric hypersurface) to order two at a general point must be an open subset of such a space.

In this paper, we establish a K\"ahlerian or projectivity criterion for a class of compact Hermitian surfaces with non-positive second Chern-Ricci curvature.

We show that a compact complex surface which admits a conformally K\"ahler metric g of positive orthogonal holomorphic bisectional curvature is biholomorphic to the complex projective plane. In addition, if g is a Hermitian metric which is…

Let $X$ be a compact Riemann surface of genus $g$ and let $x \in X$. We derive the classical presentation of $\pi_1(X,x)$ (i.e the one given by $2g$ generators $a_1,b_1, \dots, a_g,b_g$ and the relation $\prod_{i=1}^g[a_i,b_i] = 1$) from…

In this paper, we study a three-dimensional Ricci-degenerate Riemannian manifold $(M^3,g)$ that admits a smooth nonzero solution $f$ to the equation \begin{align} \label{a1a} \nabla df=\psi Rc+\phi g, \end{align} where $\psi,\phi$ are given…

A Ricci surface is defined as a Riemannian surface $(M,g_M)$ whose Gauss curvature satisfies the differential equation $K\Delta K + g_M(dK,dK) + 4K^3=0$. Andrei Moroianu and Sergiu Moroianu proved that a Ricci surface with non-positive…