Related papers: Algebraic Schouten Solitons of Three-Dimensional L…

In this paper, we compute canonical connections and Kobayashi-Nomizu connections and their curvature on three-dimensional Lorentzian Lie groups with some product structure. We define algebraic Ricci solitons associated to canonical…

In this paper, we classify affine Ricci solitons associated to canonical connections and Kobayashi-Nomizu connections and perturbed canonical connections and perturbed Kobayashi-Nomizu connections on three-dimensional Lorentzian Lie groups…

We classify Algebraic Ricci Solitons of three-dimensional Lorentzian Lie groups. All algebraic Ricci solitons that we obtain are sol-solitons. In particular, we prove that, contrary to the Riemannian case, Lorentzian Ricci solitons need not…

In this paper, we compute the Wanas tensor associated to canonical connections on three-dimensional Lorentzian Lie groups with some product structure. We define algebraic Wanas solitons associated to canonical connections. We classify…

In this paper, we classify three-dimensional Lorentzian Lie groups on which Ricci tensors associated to Bott connections, canonical connections and Kobayashi-Nomizu connections are Codazzi tensors associated to these connections. We also…

In this paper, we compute the Bott connections and their curvature on three-dimensional Lorentzian Lie groups with three different distributions, and we classify affine Ricci solitons associated to the Bott connection on three-dimensional…

In this paper, we classify Left-invariant Ricci collineations associated to canonical connections and Kobayashi-Nomizu connections on three-dimensional Lorentzian Lie groups.

We consider the linear vector Schr\"odinger equation subjected to quadratic constraints. We demonstrate that the resulting nonlinear system is closely related to the Ablowitz-Ladik hierarchy and use this fact to derive the N-soliton…

In this paper, we determine all conformal Ricci collineations associated to the Levi-Civita connection on three-dimensional Lorentzian Lie groups .

We study three-dimensional generalized Ricci solitons, both in Riemannian and Lorentzian settings. We shall determine their homogeneous models, classifying left-invariant generalized Ricci solitons on three-dimensional Lie groups.

In this note, we completely classify left-invariant Riemann solitons on three-dimensional Lorentzian Lie groups.

This paper is a survey on relations between secant identities and soliton equations and applications of soliton equations to problems of algebraic geometry, i.e., the Riemann-Schottky problem and its analogues. A short introduction into the…

We completely classify the algebraic Ricci solitons of four-dimensional pseudo-Riemannian generalized symmetric spaces.

Holonomy algebras of Weyl connections in Lorentzian signature are classified. In particular, examples of Weyl connections with all possible holonomy algebras are constructed.

We consider the universal pivotal, symmetric, monoidal, $\Bbbk$-linear category, generated by a Schurian object with a skew-symmetric multiplication, and study some of its quotients. We show that these quotients give rise to either vector…

We describe four-dimensional Lorentzian algebraic Ricci solitons. In sharp contrast with the Riemannian situation, any connected and simply connected four-dimensional Lie group admits a left-invariant Lorentz metric which is a Ricci…

A review is given of ideas in electromagnetic duality and connections to integrable field theories with soliton solutions. This leads on to a summary of recent work on Lorentzian algebras.

In this paper, we investigate the relationship between algebraic soliton metrics and soliton metrics for geometric evolution equations on Lie groups. After discussing the general relationship between algebraic soliton metrics and soliton…

In this paper we construct new classes of mixed singularities that provide realizations of real algebraic links in the $3$-sphere. Classifications and characterizations of real algebraic links are still open. These new classes of mixed…

In this paper, we completely classify three-dimensional Lorentzian $Ein(2)$ Lie groups.