Related papers: Static SKT metrics on Lie groups

Arbitrary connections on a generic Hopf algebra $H$ are studied and shown to extend to connections on tensor fields. On this ground a general definition of metric compatible connection is proposed. This leads to a sufficient criterion for…

In this paper, we provide new examples of Levi-Civita Ricci-flat Hermitian metrics on certain compact non-K\"{a}hler Calabi-Yau manifolds, including every compact Hermitian Weyl-Einstein manifold, every compact locally conformal…

In our previous work [PSSW], we showed that the Ricci flow on S^2 whose initial metric has conical singularities \sum_{j=1}^k \beta_j[p_j] converges to a constant curvature metric with conic singularities (in the stable and semi-stable…

Explicit solutions to the conifold equations with complex dimension $n=3,4$ in terms of {\it{complex coordinates (fields)}} are employed to construct the Ricci-flat K\"{a}hler metrics on these manifolds. The K\"{a}hler 2-forms are found to…

We consider d-dimensional Riemanian manifolds which admit d-2 commuting space-like Killing vector fields, orthogonal to a surface, containing two one-parametric families of light-like curves. The condition of the Ricci tensor to be zero…

We study connections on hermitian modules, and show that metric connections exist on regular hermitian modules; i.e finitely generated projective modules together with a non-singular hermitian form. In addition, we develop an index calculus…

The goal of our present paper is to deliberate $*$-conformal $\eta$-Ricci soliton within the framework of Kenmotsu manifolds. Here we have shown that a Kenmotsu metric as a $*$-conformal $\eta$-Ricci soliton is Einstein metric if the…

We show that the system of vacuum Einstein equations (i.e., Ricci-flat metrics) with two hypersurface-orthogonal, commuting Killing vector fields in $d \ge 5$ dimensions is invariant under the action of a one-parameter Lie group, and the…

Pseudo-Riemannian metrics with Levi-Civita connection in the projective class of a given torsion free affine connection can be obtained from (and are equivalent to) the maximal rank solutions of a certain overdetermined projectively…

The famous Uniformization Theorem states that on closed Riemannian surfaces there always exists a metric of constant curvature for the Levi-Cevita connection. In this article we prove that an analogue of the uniformization theorem also…

We study the existence of left invariant closed $G_2$-structures defining a Ricci soliton metric on simply connected nonabelian nilpotent Lie groups. For each one of these $G_2$-structures, we show long time existence and uniqueness of…

We show that the space of metrics of positive scalar curvature on any 3-manifold is either empty or contractible. Second, we show that the diffeomorphism group of every 3-dimensional spherical space form deformation retracts to its isometry…

Let $\pi : \mathcal X \to S$ be a local universal family of compact Ricci-flat K\"ahler manifolds over a smooth base $S$. The complexified K\"ahler cones of each fiber of the family form a holomorphic fiber bundle $\mathcal K \to S$. We…

In a Riemannian manifold with a smooth positive function that weights the associated Hausdorff measures we study stable sets, i.e., second order minima of the weighted perimeter under variations preserving the weighted volume. By assuming…

It is known that a connected and simply-connected Lie group admits only one left-invariant Riemannian metric up to scaling and isometry if and only if it is isomorphic to the Euclidean space, the Lie group of the real hyperbolic space, or…

We show that any closed biquotient with finite fundamental group admits metrics of positive Ricci curvature. Also, let M be a closed manifold on which a compact Lie group G acts with cohomogeneity one, and let L be a closed subgroup of G…

In this paper we construct solutions to Ricci DeTurck flow in four dimensions on closed manifolds which are instantaneously smooth but whose initial values $g$ are (possibly) non-smooth Riemannian metrics whose components in smooth…

We prove that the Ricci flow for complete metrics with bounded geometry depends continuously on initial conditions for finite time with no loss of regularity. This relies on our recent work where sectoriality for the generator of the…

A K\"ahler metric is called central if the determinant of its Ricci endomorphism is constant. For the case in which this constant is zero, we study on $4$-manifolds the existence of complete metrics of this type which are cohomogeneity one…

In this paper, we introduce the notions of slope stability and the Hermitian Einstein metric for big cohomology classes. The main result is the Kobayashi Hitchin correspondence on compact normal spaces with big classes admitting the…