Related papers: Four-dimensional pp-wave Lie groups and harmonic c…
We consider four dimensional Lie groups with left-invariant Riemannian metrics. For such groups we classify left-invariant conformal foliations with minimal leaves of codimension two. These foliations produce local complex-valued harmonic…
In this paper we classify those three-dimensional Riemannian Lie groups which admit harmonic morphisms to surfaces.
Harmonic functions of the three dimensional Lie groups defined on certain manifolds related to the Lie groups themselves and carrying all their unitary representations are explicitly constructed. The realisations of these Lie groups are…
A study is made of real Lie algebras admitting a hypersymplectic structure, and we provide a method to construct such hypersymplectic Lie algebras. We use this method in order to obtain the classification of all hypersymplectic structures…
A 4-dimensional Riemannian manifold equipped with an endomorphism of the tangent bundle, whose fourth power is the identity, is considered. The matrix of this structure in some basis is circulant and the structure acts as an isometry with…
We show that every n-dimensional locally homogeneous pp-wave is a plane wave, provided it is indecomposable and its curvature operator, when acting on $2$-forms, has rank greater than one. As a consequence we obtain that indecomposable,…
We consider compact oriented four-manifolds with harmonic self-dual Weyl curvature in addition to a pinching condition.
For each left-invariant Riemannian metric on simply connected nonunimodular Lie groups of dimension four, we determine the full group of isometries.
We consider 5-dimensional Lie groups with left-invariant Riemannian metrics. For such groups we give a partial classification of left-invariant conformal foliations with minimal leaves of codimension 2. These foliations produce local…
An example of a four-dimensional special complex manifold with Norden metric of constant holomorphic sectional curvature is constructed via a two-parametric family of solvable Lie algebras. The curvature properties of the obtained manifold…
We show that any left invariant metric with harmonic curvature on a solvable Lie group is Ricci-parallel. We show the same result for any Lie group of dimension $\leq$ 6.
We consider a $4$-dimensional Riemannian manifold $M$ equip\-ped with a circulant structure $q$, which is an isometry with respect to the metric $g$ and $q^{4}=\id$, $q^{2}\neq \pm \id$. For such a manifold $(M, g, q)$ we obtain some…
In this paper, we give the defination of harmonic curvature function some special curves such as helix, slant curves, Mannheim curves and Bertrand curves. Then, we recall the characterizations of helices [8], slant curves (see [19]) and…
In this paper we classify all four dimensional real Lie bialgebras of symplectic type. The classical r- matrices for these Lie bialgebras and Poisson structures on all of the related four dimensional Poisson-Lie groups are also obtained.…
We construct 4-dimensional Riemannian Lie groups carrying left-invariant conformal foliations with minimal leaves of codimension 2. We show that these foliations are holomorphic with respect to an (integrable) Hermitian structure which is…
A classical pp-wave is a 4-dimensional Lorentzian spacetime which admits a nonvanishing parallel spinor field; here the connection is assumed to be Levi-Civita. We generalise this definition to metric compatible spacetimes with torsion and…
By considering suitable Poisson groupoids, we develop an approach to obtain Lie group structures on (subgroups of) the Poisson diffeomorphism groups of various classes of Poisson manifolds. As applications, we show that the Poisson…
We determine the structure of solvable Lie groups endowed with invariant stretched non-positive Weyl connections and find classes of solvable Lie groups admitting and not admitting such connections. In dimension 4 we fully classify solvable…
It is possible to construct representations of the Lorentz group using four-dimensional harmonic oscillators. This allows us to construct three-dimensional wave functions with the usual rotational symmetry for space-like coordinates and…
The automorphisms of all 4-dimensional, real Lie Algebras are presented in a comprehensive way. Their action on the space of $4\times 4$, real, symmetric and positive definite, matrices, defines equivalence classes which are used for the…