Related papers: Distinguished G2-structures on solvmanifolds

These notes have been prepared for the Workshop on "(Non)-existence of complex structures on $\mathbb{S}^6$", to be celebrated in Marburg in March, 2017. The material is not intended to be original. It contains a survey about the smallest…

We study the stability of non compact steady and expanding gradient Ricci solitons. We first show that strict linear stability implies dynamical stability. Then we give various sufficient geometric conditions ensuring the strict linear…

We prove an existence result for local and global G-structure preserving affine immersions between affine manifolds. Several examples are discussed in the context of Riemannian and semi-Riemannian geometry, including the case of isometric…

We introduce a new curvature-pinching condition, which is weaker than the positive sectional curvature or PIC1, and then we prove several rigidity results for the rotationally symmetric solutions of steady Ricci solitons, i.e., the Bryant…

We investigate the topology of the compact hypersurfaces in round spheres whose Ricci curvature satisfies an appropriate bound that only depends on the mean curvature of the submanifold. In this paper, the use of the Bochner technique…

This article introduces the problem of finding intrinsic torsion varieties associated to G-structures on a fixed parallelizable Riemannian manifold. As an illustration, the intrinsic torsion varieties of orthogonal almost product structures…

There are studied in details 5-dimensional pseudo-Riemannian manifolds equipped with the structure analogous to the almost cosymplectic (almost coKaehler) structure. The curvature by assumption commutes with the structure affinor and all…

A complete study of the structure of Ricci collineations for type B warped spacetimes is carried out. This study can be used as a method to obtain these symetries in such spacetimes. Special cases as 2+2 reducible spacetimes, and plane and…

We generalize the classical construction principles of infinite-dimensional real (and complex) Lie groups to the case of Lie groups over non-discrete topological fields. In particular, we discuss linear Lie groups, mapping groups, test…

There are five unimodular simply connected three dimensional unimodular non abelian Lie groups: the nilpotent Lie group $\mathrm{Nil}$, the special unitary group $\mathrm{SU}(2)$, the universal covering group…

We study left invariant locally conformally product structures on simply connected Lie groups and give their complete description in the solvable unimodular case. Based on previous classification results, we then obtain the complete list of…

The object of the present paper is to study some types of Ricci pseudosymmetric $(LCS)_n$-manifolds whose metric is Ricci soliton. We found the conditions when Ricci soliton on concircular Ricci pseudosymmetric, projective Ricci…

In stark contrast to lower dimensions, we produce a plethora of ancient and immortal Ricci flows in real dimension $4$ with Einstein orbifolds as tangent flows at infinity. For instance, for any $k\in\mathbb{N}_0$, we obtain continuous…

Homogeneous compatible almost complex structures on symplectic manifolds are studied, focusing on those which are special, meaning that their Chern-Ricci form is a multiple of the symplectic form. Non Chern-Ricci flat ones are proven to be…

In this article, we consider an orthogonal decomposition of the traceless part of the Ricci tensor of a compact Riemannian manifold and study its application to the geometry of compact almost Ricci solitons. In addition, we consider an…

We demonstrate that any four-dimensional shrinking Ricci soliton $(\mathcal B \times {\mathbb S^2}, g)$, where $\mathcal B$ is any two-dimensional complete noncompact surface and $g$ is a warped product metric over the base $\mathcal B$,…

This is a short presentation of some classical results on finite dimensional complex Lie algebras (classification of nilpotent Lie algebras, deformations and perturbations, contractions and rigidity). We present some applications to…

We describe the local structure of self-dual gradient Ricci solitons in neutral signature. If the Ricci soliton is non-isotropic then it is locally conformally flat and locally isometric to a warped product of the form $I\times_\varphi…

We classify solvable Lie groups admitting left invariant symplectic half-flat structure. When the Lie group has a compact quotient by a lattice, we show that these structures provide solutions of supersymmetric equations of type IIA.

Important models for immortal solutions of Ricci flow that collapse with bounded curvature come from locally G-invariant solutions on principal bundles, where G is a nilpotent Lie group. In this paper, we establish convergence and…