31 citations · 104 across the 11 of their papers we have counts for
11 papers
On geodesic orbit nilmanifolds
Yu. G. Nikonorov
The paper is devoted to the study of geodesic orbit Riemannian metrics on nilpotent Lie groups. The main result is the construction of continuous families of pairwise non-isomorphi…
On a characterization of critical points of the scalar curvature functional
Yu. G. Nikonorov
This is an English translation of the following paper, published several years ago: Nikonorov Yu.G. On a characterization of critical points of the scalar curvature functional (Rus…
Compact geodesic orbit spaces with a simple isotropy group
Z. Chen, Y. Nikolayevsky, Yu. Nikonorov
Let be a compact, simply connected, Riemannian homogeneous space, where is (almost) effective and is a simple Lie group. In this paper, we first classify all -na…
Algebraic properties of bounded Killing vector fields
Ming Xu, Yu. G. Nikonorov
In this paper, we consider a connected Riemannian manifold where a connected Lie group acts effectively and isometrically. Assume defines…
Spectral properties of Killing vector fields of constant length
Yu. G. Nikonorov
This paper is devoted to the study of properties of Killing vector fields of constant length on Riemannian manifolds. If is a Lie algebra of Killing vector fields on…
Geodesic Orbit Riemannian Structures on
Carolyn S. Gordon, Yuriĭ G. Nikonorov
A geodesic orbit manifold is a complete Riemannian manifold all of whose geodesics are orbits of one-parameter groups of isometries. We give both a geometric and an algebraic chara…
On invariant Riemannian metrics on Ledger-Obata spaces
Y. Nikolayevsky, Yu. G. Nikonorov
We study invariant metrics on Ledger-Obata spaces . We give the classification and an explicit construction of all naturally reductive metrics, and also show…
On left-invariant Einstein Riemannian metrics that are not geodesic orbit
Yu. G. Nikonorov
In this paper we prove that the compact Lie group admits a left-invariant Einstein metric that is not geodesic orbit. In order to prove the required assertion, we develop som…
On the structure of geodesic orbit Riemannian spaces
Yu. G. Nikonorov
The paper is devoted to the study of geodesic orbit Riemannian spaces that could be characterize by the property that any geodesic is an orbit of a 1-parameter group of isometries.…
The signature of the Ricci curvature of left invariant Riemannian metrics on 4-dimensional Lie groups
A. G. Kremlyov, Yu. G. Nikonorov
In this paper, we present the classification of all possible signatures of the Ricci curvature of left-invariant Riemannian metrics on 4-dimensional Lie groups and discuss some rel…
Invariant Einstein metrics on some homogeneous spaces of classical Lie groups
Andreas Arvanitoyeorgos, V. V. Dzhepko, YU. G. Nikonorov
A Riemannian manifold is called Einstein if the metric satisfies the condition $\Ric (ρ)=c\cdot ρ$ for some constant . This paper is devoted to the investigation of…