Related papers: Multicontact mappings on Hessenberg manifolds

We investigate the local geometry of a pair of independent contact structures on 3-manifolds under maps that independently preserve each contact structure. We discover that such maps are homotheties on the contact 1-forms and we discover…

This paper is devoted to the study of geometric structures modeled on homogeneous spaces G/P, where G is a real or complex semisimple Lie group and $P\subset G$ is a parabolic subgroup. We use methods from differential geometry and very…

Let $\mathfrak{g}$ be a real semisimple Lie algebra with Iwasawa decomposition $\mathfrak{k} \oplus \mathfrak{a} \oplus \mathfrak{n}$. We show that, except for some explicit exceptional cases, every derivation of the nilpotent subalgebra…

It was proven by Hitchin that any solution of his evolution equations for a half-flat SU(3)-structure on a compact six-manifold M defines an extension of M to a seven-manifold with holonomy in G_2. We give a new proof, which does not…

Let (M, g) be a pseudo Riemannian manifold. We consider four geometric structures on M compatible with g: two almost complex and two almost product structures satisfying additionally certain integrability conditions. For instance, if r is a…

In the paper "The Second cohomology of nilpotent orbits in classical Lie algebras, Kyoto J. Math. 60 (2020), no. 2, 717-799" by I. Biswas, P. Chatterjee and C. Maity homotopy types of nilpotent orbits are explicitly described in the case of…

In this article, we study compactifications of homogeneous spaces coming from equivariant, open embeddings into a generalized flag manifold $G/P$. The key to this approach is that in each case $G/P$ is the homogeneous model for a parabolic…

We have studied irreducible real (respectively, quaternionic) Lie algebroid connections and prove that the Gauge theoretic moduli space has Hausdorff Hilbert manifold structure. This work generalises some known results about simple…

We prove that, for some classes of complex nilmanifolds, the Bott-Chern cohomology is completely determined by the Lie algebra associated to the nilmanifold with the induced complex structure. We use these tools to compute the Bott-Chern…

Let $G$ be a connected, simply connected one-parameter metabelian nilpotent Lie group, that means, the corresponding Lie algebra has a one-codimensional abelian subalgebra. In this article we show that $G$ contains a discrete cocompact…

In an earlier paper we developed the classification of weakly symmetric pseudo--riemannian manifolds $G/H$ where $G$ is a semisimple Lie group and $H$ is a reductive subgroup. We derived the classification from the cases where $G$ is…

We continue the study of the distribution of closed geodesics on nilmanifolds constructed from a simply connected 2-step nilpotent Lie group with a left invariant metric and a lattice. We consider a Lie group with an associated 2-step…

In this paper, we consider a closed Riemannian manifold $M^{n+1}$ with dimension $3\leq n+1\leq 7$, and a compact Lie group $G$ acting as isometries on $M$ with cohomogeneity at least $3$. After adapting the Almgren-Pitts min-max theory to…

We study complete, connected and simply connected $n$-dim Riemannian manifold $M$ satisfying Ricci curvature lower bound. Further more, suppose that $M$ admits discrete isometric group actions $G$ so that the diameter of the quotient space…

Almost paracontact manifolds of an odd dimension having an almost paracomplex structure on the paracontact distribution are studied. The components of the fundamental (0,3)-tensor, derived by the covariant derivative of the structure…

Let G be a noncompact real semisimple Lie group. The regular coadjoint orbits of G can be partitioned into a finite set of types. We show that on each regular orbit, the Iwasawa decomposition induces a left-invariant foliation which is…

We present an approach to Jacobi and contact geometry that makes many facts, presented in the literature in an overcomplicated way, much more natural and clear. The key concepts are Kirillov manifolds and linear Kirillov structures, i.e.,…

Two groups are virtually isomorphic if they can be obtained one from the other via a finite number of steps, where each step consists in taking a finite extension or a finite index subgroup (or viceversa). Virtually isomorphic groups are…

We answer in the affirmative a question posed by Ivanov and Vassilev on the existence of a seven dimensional quaternionic contact manifold with closed fundamental 4-form and non-vanishing torsion endomorphism. Moreover, we show an approach…

We consider Lie groups equipped with arbitrary distances. We only assume that the distance is left-invariant and induces the manifold topology. For brevity, we call such object metric Lie groups. Apart from Riemannian Lie groups,…