6 papers
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…