Related papers: Aspects of the Levi form
We study the behavior of connections and curvature under the HK/QK correspondence, proving simple formulae expressing the Levi-Civita connection and Riemann curvature tensor on the quaternionic K\"ahler side in terms of the initial…
An explicit classification of simply connected compact homogeneous CR manifolds G/L of codimension one, with non-degenerate Levi form, is given. There are three classes of such manifolds: a) the standard CR homogeneous manifolds which are…
We study CR hypersurfaces in $\mathbb{C}^4$ that are Levi degenerate with constant rank Levi form, and moreover finitely nondegenerate. Each of these can be described as a deformation of a model CR hypersurface by adding terms of higher…
We show that the maximal prolongation of a certain algebra associated with a non-degenerate Hermitian form on ${\Bbb C}^n\times{\Bbb C}^n$ with values in ${\Bbb R}^k$ is canonically isomorphic to the Lie algebra of infinitesimal holomorphic…
We give a complete description of the vertex algebra of global sections of the chiral de Rham complex of an arbitrary compact Ricci-flat K\"ahler manifold.
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…
On an equation associated with the contact Lie algebras/ Mikhail V. Saveliev/ In the framework of a Lie algebraic approach we study a nonlinear equation associated with the contact Lie algebra ${\bf K}K_m$, that seems to be relavant for…
We present a compared analysis of some properties of indefinite almost $\mathcal{S}$-manifolds and indefinite $\mathcal{S}$-manifolds. We give some characterizations in terms of the Levi-Civita connection and of the characteristic vector…
We construct examples of non-formal simply connected and compact oriented manifolds of any dimension bigger or equal to 7.
A singular real analytic foliation $\mathcal{F}$ of real codimension one on an $n$-dimensional complex manifold $M$ is Levi-flat if each of its leaves is foliated by immersed complex manifolds of dimension $n-1$. These complex manifolds are…
We introduce $q$-deformed connections on the quantum 2-sphere and 3-sphere, satisfying a twisted Leibniz rule in analogy with $q$-deformed derivations. We show that such connections always exist on projective modules. Furthermore, a…
We construct many examples of Lie groups with compact Levi factor admitting a left-invariant metric with negative Ricci curvature. We start with a Lie algebra with Levi factor su(n) or so(n) acting on an abelian nilradical via the…
In this paper, we conclude the geometric structures in $Sol_3$ with the Levi-Civita connection and the semi-symmetric non-metric connection. We discuss two special cases to study the geometric structures in $Sol_3$ with the semi-symmetric…
The basic class of the non-integrable almost complex manifolds with Norden metric is considered. Its curvature properties are studied. The isotropic Kaehler type of investigated manifolds is introduced and characterized geometrically.
We survey results on compact Clifford-Klein forms of homogeneous spaces, with a focus on recent contributions and organized around approaches via topology, geometry and dynamics. In addition, we survey results on moduli spaces of compact…
We classify the germs of $\mathcal{C}^\infty$ CR manifolds that admit a smooth CR contraction. We show that such a CR manifold is embedded into $\CC^n$ as a real hypersurface defined by a polynomial defining function consisting of monomials…
We study formal deformations of hom-Lie-Rinehart algebras. The associated deformation cohomology that controls deformations is constructed using multiderivations of hom-Lie-Rinehart algebras.
In this article, we develop foundational theory for geometries of the space of closed $G_2$-structures in a given cohomology class as an infinite-dimensional manifold. We introduce Sobolev-type metrics, construct their Levi-Civita…
The generalized Casimir invariants of real indecomposable Lie algebras admitting a nontrivial Levi decomposition are determined.
In this paper, we show that the CR $Q$-curvature is orthogonal to the space of CR pluriharmonic functions on any closed strictly pseudoconvex CR manifold of dimension at least five. To this end, we obtain a cohomological expression of the…