相关论文: Pseudo-Riemannian Sasaki solvmanifolds

In the presented paper left-invariant pseudo-Riemannian metrics on four-dimensional Lie groups with zero Schouten-Weyl tensor are investigated. The complete classification of these metric Lie groups is obtained in terms of the structure…

We study the isometry groups and Killing vector fields of a family of pseudo-Riemannian metrics on Euclidean space which have neutral signature (3+2p,3+2p). All are p+2 curvature homogeneous, all have vanishing Weyl scalar invariants, all…

We provide examples of naturally reductive pseudo-Riemannian spaces, in particular an example of a naturally reductive pseudo-Riemannian 2-step nilpotent Lie group $(N, < \,,\,>_N)$, such that $< \,,\,>_N$ is invariant under a left action…

We study some applications of solvable Lie algebras in type IIA, type IIB and M theories. RR and NS generators find a natural geometric interpretation in this framework. Special emphasis is given to the counting of the abelian nilpotent…

We construct the normal forms of null-K\"ahler metrics: pseudo-Riemannian metrics admitting a compatible parallel nilpotent endomorphism of the tangent bundle. Such metrics are examples of non-Riemannian holonomy reduction, and (in the…

In this paper, we study the solvmanifolds constructed from any parabolic subalgebras of any semisimple Lie algebras. These solvmanifolds are naturally homogeneous submanifolds of symmetric spaces of noncompact type. We show that the Ricci…

Let G be a nontrivial finite subgroup of U(m) acting freely on C^m - 0. Then C^m/G has an isolated quotient singularity at 0. Let X be a resolution of C^m/G, and g a Kahler metric on X. We say that g is Asymptotically Locally Euclidean…

Riemannian Einstein solvmanifolds can be described in terms of nilsolitons, namely nilpotent Lie groups endowed with a left-invariant Ricci soliton metric. This characterization does not extend to indefinite metrics; nonetheless,…

Almost contact complex Riemannian manifolds, known also as almost contact B-metric manifolds, are in principle equipped with a pair of mutually associated pseudo-Riemannian metrics. Each of these metrics is specialized here as a Yamabe…

Four dimensional simply connected Lie groups admitting a pseudo K\"ahler metric are determined. The corresponding Lie algebras are modelized and the compatible pairs $(J,\omega)$ are parametrized up to complex isomorphism (where $J$ is a…

This is a collection of notes on the properties of left-invariant metrics on the eight-dimensional compact Lie group SU(3). Among other topics we investigate the existence of invariant pseudo-Riemannian Einstein metrics on this manifold. We…

We construct homogeneous flat pseudo-Riemannian manifolds with non-abelian fundamental group. In the compact case, all homogeneous flat pseudo-Riemannian manifolds are complete and have abelian linear holonomy group. To the contrary, we…

This work deals with the structure of the isometry group of pseudo-Riemannian 2-step nilmanifolds. We study the action by isometries of several groups and we construct examples showing substantial differences with the Riemannain situation;…

The problem of classification of connected holonomy groups (equivalently of holonomy algebras) for pseudo-Riemannian manifolds is open. The classification of Riemannian holonomy algebras is a classical result. The classification of…

We define a class of Riemannian and pseudo-Riemannian 2-step nilpotent Lie groups with nondegenerate centers that generalize the H-type groups of Kaplan. Examples are given and geometric properties are investigated.

We give the complete classification of left-invariant sub-Riemannian structures on three dimensional Lie groups in terms of the basic differential invariants. This classifications recovers other known classification results in the…

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 study Lorentzian manifolds $(M, g)$ of dimension $n\geq 4$, equipped with a maximally twisting shearfree null vector field $p_o$, for which the leaf space $S = M/\{\exp t p_o\}$ is a smooth manifold. If $n = 2k$, the quotient $S =…

The Hessian geometry is the real analogue of the K\"ahler one. Sasakian geometry is an odd-dimensional counterpart of the K\"ahler geometry. In the paper, we study the connection between projective Hessian and Sasakian manifolds analogous…

Given a K\"ahler manifold $(Z,J,\omega)$ and a compact real submanifold $M\subset Z$, we study the properties of the gradient map associated with the action of a noncompact real reductive Lie group ${\rm G}$ on the space of probability…