Related papers: Neutral bi-Hermitian Gray surfaces

The fixed points of the generalized Ricci flow are the Bismut Ricci flat metrics, i.e., a generalized metric $(g,H)$ on a manifold $M$, where $g$ is a Riemannian metric and $H$ a closed $3$-form, such that $H$ is $g$-harmonic and…

In this paper we study 4-dimensional $(m,\rho)$-quasi-Einstein manifolds with harmonic Weyl curvature when $m\notin\{0,\pm1,-2,\pm\infty\}$ and $\rho\notin\{\frac{1}{4},\frac{1}{6}\}$. We prove that a non-trivial $(m,\rho)$-quasi-Einstein…

A gap in the proof of the main result in reference [1] in our original submission propagated into the constructions presented in the first version of our manuscript. In this version we give an alternative proof for the existence of…

For a compact connected Lie group $G$ we study the class of bi-invariant affine connections whose geodesics through $e\in G$ are the 1-parameter subgroups. We show that the bi-invariant affine connections which induce derivations on the…

In this paper, we study several types of geometric problems related to the Ricci curvature on noncompact complex manifolds, such as the existence of K\"{a}hler-Einstein metrics on complete K\"{a}hler manifolds with negative Ricci curvature,…

We study biharmonic hypersurfaces in a generic Riemannian manifold. We first derive an invariant equation for such hypersurfaces generalizing the biharmonic hypersurface equation in space forms studied in \cite{Ji2}, \cite{CH}, \cite{CMO1},…

We show that the isoperimetric profile $h_{g(t)}(\xi)$ of a compact Riemannian manifold $(M,g)$ is jointly continuous when metrics $g(t)$ vary continuously. We also show that, when $M$ is a compact surface and $g(t)$ evolves under…

Inspired by soliton models, we propose a description of static particles in terms of Riemannian 4-manifolds with self-dual Weyl tensor. For electrically charged particles, the 4-manifolds are non-compact and asymptotically fibred by circles…

In the present paper, we show that on a compact Riemannian manifold $(M,g)$ of dimension $d\leqslant 4$ whose metric has negative curvature, the renormalized partition function $Z_g(\lambda)$ of a massive Gaussian Free Field determines the…

This article proves that if M is a smooth manifold of dimension at least four, then for generic choice of metric on M, all prime parametrized minimal surfaces in M are free of branch points and lie on nondegenerate critical submanifolds for…

We show that the combination of non-negative sectional curvature (or $2$-intermediate Ricci curvature) and strict positivity of scalar curvature forces rigidity of complete (non-compact) two-sided stable minimal hypersurfaces in a…

In this paper, we prove that if a compact K\"ahler manifold $X$ has a smooth Hermitian metric $\omega$ such that $(T_X,\omega)$ is uniformly RC-positive, then $X$ is projective and rationally connected. Conversely, we show that, if a…

We construct new homogeneous Einstein spaces with negative Ricci curvature in two ways: First, we give a method for classifying and constructing a class of rank one Einstein solvmanifolds whose derived algebras are two-step nilpotent. As an…

We consider a closed cohomogeneity one Riemannian manifold $(M^n,g) $ of dimension $n\geq 3$. If the Ricci curvature of $M$ is positive, we prove the existence of infinite nodal solutions for equations of the form $-\Delta_g u + \lambda u =…

We characteristize those Einstein four manifolds which are locally symmetric spaces of noncompact type. Namely they are four manifolds which admit solutions to the (non-Abelian) Seiberg Witten equations and satisty certain characterisitc…

Let (M,h) be a compact 4-dimensional Einstein manifold, and suppose that h is Hermitian with respect to some complex structure J on M. Then either (M,J,h) is Kaehler-Einstein, or else, up to rescaling and isometry, it is one of the…

Any 7-dimensional cocalibrated G_2-manifold admits a unique connection $\nabla$ with skew symmetric torsion. We study these manifolds under the additional condition that the $\nabla$-Ricci tensor vanishes. In particular, we describe their…

We study the size of the isometry group Isom(M, g) of Riemannian manifolds (M, g) as g varies. For M not admitting a circle action, we show that the order of Isom(M, g) can be universally bounded in terms of the bounds on Ricci curvature,…

This work proves certain general orbifold compactness results for spaces of Riemannian metrics, generalizing earlier results along these lines for Einstein metrics or metrics with bounded Ricci curvature. This is then applied to prove such…

We give some rigidity theorems for an n$(\geq4)$-dimensional compact Riemannian manifold with harmonic Weyl curvature, positive scalar curvature and positive constant $\sigma_2$. Moreover, when $n=4,$ we prove that a 4-dimensional compact…