13 citations · 73 across the 38 of their papers we have counts for
30 papers · 1 filter
On weakly Einstein Lie groups
Yunhee Euh, Sinhwi Kim, Yuri Nikolayevsky +1
A Riemannian manifold is called \emph{weakly Einstein} if the tensor is a scalar multiple of the metric tensor . We consider weakly Einstein Lie gro…
Weakly Einstein hypersurfaces in space forms
Jihun Kim, Yuri Nikolayevsky, JeongHyeong Park
A Riemannian manifold is called \emph{weakly Einstein} if the tensor is a scalar multiple of the metric tensor . We give a complete classifi…
Pseudo-Riemannian geodesic orbit nilmanifolds of signature
Zhiqi Chen, Yuri Nikolayevsky, Joseph A. Wolf +1
The geodesic orbit property is useful and interesting in itself, and it plays a key role in Riemannian geometry. It implies homogeneity and has important classes of Riemannian mani…
The Structure of Geodesic Orbit Lorentz Nilmanifolds
Yuri Nikolayevsky, Joseph A. Wolf
The geodesic orbit property is useful and interesting in Riemannian geometry. It implies homogeneity and has important classes of Riemannian manifolds as special cases. Those class…
Respectful decompositions of Lie algebras
Grant Cairns, Yuri Nikolayevsky
One of Pierre Molino's principal mathematical achievements was his theory of Riemannian foliations. One of his last papers, published in 2001, showed that his theory could be exten…
Stability of geodesic vectors in low-dimensional Lie algebras
An Ky Nguyen, Yuri Nikolayevsky
A naturally parameterised curve in a Lie group with a left invariant metric is a geodesic, if its tangent vector left-translated to the identity satisfies the Euler equation $\dot{…
Einstein hypersurfaces in irreducible symmetric spaces
Yuri Nikolayevsky, JeongHyeong Park
We show that if is an Einstein hypersurface in an irreducible Riemannian symmetric space of rank greater than (the classification in the rank-one case was pr…
On 2-stein submanifolds in space forms
Yunhee Euh, Jihun Kim, Yuri Nikolayevsky +1
We prove that a 2-stein submanifold in a space form whose normal connection is flat or whose codimension is at most 2, has constant curvature.
Einstein hypersurfaces of Damek-Ricci spaces
Sinhwi Kim, Yuri Nikolayevsky, JeongHyeong Park
Einstein hypersurfaces are ``very rare" in rank-one symmetric spaces. Damek-Ricci spaces may be viewed as the closest and the most natural generalisations of noncompact rank-one sy…
Totally geodesic submanifolds of Damek-Ricci spaces and Einstein hypersurfaces of the Cayley projective plane
Sinhwi Kim, Yuri Nikolayevsky, JeongHyeong Park
We classify totally geodesic submanifolds of Damek-Ricci spaces and show that they are either homogeneous (such submanifolds are known to be "smaller" Damek-Ricci spaces) or isomet…
Einstein extensions of Riemannian manifolds
D. Alekseevsky, Y. Nikolayevsky
Given a Riemannian space of dimension and a field of symmetric endomorphisms on , we define the extension of by to be the Riemannian manifold of dimensio…
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…
Compact pseudo-Riemannian homogeneous Einstein manifolds of low dimension
Wolfgang Globke, Yuri Nikolayevsky
Let be pseudo-Riemannian homogeneous Einstein manifold of finite volume, and suppose a connected Lie group acts transitively and isometrically on . In this situation, th…
-contact unit tangent sphere bundles of Riemannian manifolds
Yuri Nikolayevsky, Jeong Hyeong Park
A contact metric manifold is said to be -contact, if the characteristic vector field is harmonic. We prove that the unit tangent bundle of a Riemannian manifold equipped wit…
Locally conformally Berwald manifolds and compact quotients of reducible manifolds by homotheties
Vladimir S. Matveev, Yuri Nikolayevsky
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 cha…
Curvature properties of metric nilpotent Lie algebras which are independent of metric
G. Cairns, A. Hinić Galić, Y. Nikolayevsky
This paper consists of two parts. First, motivated by classic results, we determine the subsets of a given nilpotent Lie algebra (respectively, of the Grassmannian o…
Solvable extensions of negative Ricci curvature of filiform Lie groups
Y. Nikolayevsky
We give necessary and sufficient conditions of the existence of a left-invariant metric of strictly negative Ricci curvature on a solvable Lie group the nilradical of whose Lie alg…
A counterexample to Belgun-Moroianu conjecture
Vladimir S. Matveev, Yuri Nikolayevsky
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…
Geodesic Bases for Lie Algebras
Grant Cairns, Ana Hinić Galić, Yuri Nikolayevsky +1
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 non-existenc…
On the existence of orthonormal geodesic bases for Lie algebras
Grant Cairns, Nguyen Thanh Tung Le, Anthony Nielsen +1
We show that every unimodular Lie algebra, of dimension at most 4, equipped with an inner product, possesses an orthonormal basis comprised of geodesic elements. On the other hand,…
A note on Rakić duality principle for Osserman manifolds
Y. Nikolayevsky, Z. Rakić
In this note we prove that for a Riemannian manifold the Osserman pointwise condition is equivalent to the Rakić duality principle.
Totally Geodesic Subalgebras of Filiform Nilpotent Lie algebras
Grant Cairns, Ana Hinić Galić, Yuri Nikolayevsky
We determine the maximal dimension of totally geodesic subalgebras of N-graded filiform Lie algebras, and we show that these bounds are attained.
Totally Geodesic Subalgebras of Nilpotent Lie algebras
Grant Cairns, Ana Hinić Galić, Yuri Nikolayevsky
A metric Lie algebra g is a Lie algebra equipped with an inner product. A subalgebra h of a metric Lie algebra g is said to be totally geodesic if the Lie subgroup corresponding to…
Weyl homogeneous manifolds modeled on compact Lie groups
Y. Nikolayevsky
A Riemannian manifold is called Weyl homogeneous, if its Weyl tensors at any two points are "the same", up to a positive multiple. A Weyl homogeneous manifold is modeled on a homog…