9 citations · 12 across the 7 of their papers we have counts for
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Locally symmetric hypersurfaces in globally symmetric spaces
Jihun Kim, Yuri Nikolayevsky, Ruy Tojeiro
We classify locally symmetric hypersurfaces, understood in the intrinsic sense, in Riemannian globally symmetric spaces.
Hypersurfaces with constant sectional curvature of a product of two space forms
Jihun Kim, Yuri Nikolayevsky, Ruy Tojeiro
We complete the classification of hypersurfaces with constant sectional curvature of dimension greater than or equal to three in the product of two space forms.
Quadratic Killing tensors on some symmetric spaces of higher rank
An Ky Nguyen, Yuri Nikolayevsky
All Killing tensor fields on the spaces of constant curvature and on the complex projective space are decomposable, that is, can be represented as the sum of symmetric tensor produ…
Killing tensors on projective spaces
Owen Dearricott, Yuri Nikolayevsky
A Killing tensor field on a Riemannian space corresponds to an integral of the geodesic flow polynomial in momenta. A (contravariant) Killing tensor field is called \emph{decomposa…
Quadratic Killing tensors on classical Lie groups are decomposable
Vladimir Matveev, An Ky Nguyen, Yuri Nikolayevsky
A Killing tensor field on a Riemannian manifold is a covariant symmetric tensor field whose contraction with the velocity vector along a geodesic produces a homogeneous pol…
On Killing tensors on Riemannian symmetric spaces
Vladimir Matveev, Yuri Nikolayevsky
A Killing tensor field on a Riemannian space corresponds to an integral of the geodesic flow polynomial in momenta. A Killing tensor field is called decomposable if it is a polynom…
Non-singular geodesic orbit nilmanifolds
Yuri Nikolayevsky, Wolfgang Ziller
A Riemannian manifold is called a geodesic orbit manifolds, GO for short, if any geodesic is an orbit of a one-parameter group of isometries. By a result of C.Gordon, a non-flat GO…
Non-singular weakly symmetric nilmanifolds
Y. Nikolayevsky, W. Ziller
A Riemannian manifold is called weakly symmetric if any two points in can be interchanged by an isometry. The compact ones have been well understood, and the main remaining…
Killing tensors on reducible spaces
Vladimir S. Matveev, Yuri Nikolayevsky
We prove that on the product of two Riemannian manifolds one of which is compact, any Killing tensor is reducible, that is, is the sum of products of Killing tensors on the factors…
Quadratic Killing tensors on symmetric spaces which are not generated by Killing vector fields
Vladimir S. Matveev, Yuri Nikolayevsky
Every Killing tensor field on the space of constant curvature and on the complex projective space can be decomposed into the sum of symmetric tensor products of Killing vector fiel…
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…