Yuri Nikolayevsky

On solvable Lie groups of negative Ricci curvature

We study solvable Lie groups which admit a left-invariant metric of strictly negative Ricci curvature. We obtain necessary and sufficient conditions of the existence of such a metric for Lie groups the nilradical of whose Lie algebra is either abelian or Heisenberg or standard filiform and discuss some open questions.

Geodesic bases for Lie algebras

For finite dimensional real Lie algebras, we investigate the existence of an inner product having a basis comprised of geodesic elements. We give several existence and nonexistence results in certain cases: unimodular solvable Lie algebras having an abelian nilradical, algebras having an abelian derived algebra, algebras having a codimension one ideal of a particular kind, nonunimodular algebras of dimension and unimodular algebras of dimension .

A counterexample to Belgun–Moroianu conjecture

Abstract We construct an example of a closed manifold with a nonflat reducible locally metric connection such that it preserves a conformal structure and such that it is not the Levi-Civita connection of a Riemannian metric.

A sharp refinement of a result of Zverovich-Zverovich

For a finite sequence of positive integers to be the degree sequence of a finite graph, Zverovich and Zverovich gave a sufficient condition involving only the length of the sequence, its largest entry and its smallest entry. Barrus, Hartke, Jao, and West gave a better bound and showed that the sharp bound is never less than theirs by more than 1. In this paper we determine the sharp bound.

Locally conformally Berwald manifolds and compact quotients of reducible manifolds by homotheties@@@Variétés localement conformément Berwaldiennes et quotients compacts de variétés réductibles par d’homothéthies

We study locally conformally Berwald metrics on closed manifolds which are not globally conformally Berwald. We prove that the characterization of such metrics is equivalent to characterizing incomplete, simply-connected, Riemannian manifolds with reducible holonomy group whose quotient by a group of homotheties is closed. We further prove a de Rham type splitting theorem which states that if such a manifold is analytic, it is isometric to the Riemannian product of a Euclidean space and an incomplete manifold.

Great-circle spherical thrackles

We establish Conways thrackle conjecture in the case of great-circle thrackles; that is, for drawings on the unit sphere where the edges are arcs of great circles.

Compact pseudo-Riemannian homogeneous Einstein manifolds of low dimension

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A sufficient condition for a pair of sequences to be bipartite graphic

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On invariant Riemannian metrics on Ledger–Obata spaces

be pseudo-Riemannian homogeneous Einstein manifold of finite volume, and suppose a connected Lie group

Conewise Linear Periodic Maps of the Plane with Integer Coefficients

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