Hidden symmetries in a gauge covariant approach, Hamiltonian reduction and oxidation

Hidden symmetries in a covariant Hamiltonian formulation are investigated involving gauge covariant equations of motion. The special role of the Stackel-Killing tensors is pointed out. A reduction procedure is used to reduce the original phase space to another one in which the symmetries are divided out. The reverse of the reduction procedure is done by stages performing the unfolding of the gauge transformation followed by the Eisenhart lift in connection with scalar potentials.Comment: 15 pages; based on a talk at QTS-7 Conference, Prague, August 7-13, 201

Killing forms on the five-dimensional Einstein-Sasaki Y(p,q) spaces

We present the complete set of Killing-Yano tensors on the five-dimensional Einstein-Sasaki Y(p,q) spaces. Two new Killing-Yano tensors are identified, associated with the complex volume form of the Calabi-Yau metric cone. The corresponding hidden symmetries are not anomalous and the geodesic equations are superintegrable.Comment: 10 pages; improved versio

The Dirac equation in Taub-NUT space

Using chiral supersymmetry, we show that the massless Dirac equation in the Taub-NUT gravitational instanton field is exactly soluble and explain the arisal and the use of the dynamical (super) symmetry.Comment: An importatn misprint in a reference is corrected. Plain Tex. 8 page

Dynamical algebra and Dirac quantum modes in Taub-NUT background

The SO(4,1) gauge-invariant theory of the Dirac fermions in the external field of the Kaluza-Klein monopole is investigated. It is shown that the discrete quantum modes are governed by reducible representations of the o(4) dynamical algebra generated by the components of the angular momentum operator and those of the Runge-Lenz operator of the Dirac theory in Taub-NUT background. The consequence is that there exist central and axial discrete modes whose spinors have no separated variables.Comment: 17 pages, latex, no figures. Version to appear in Class.Quantum Gra

Generalized Killing equations and Taub-NUT spinning space

The generalized Killing equations for the configuration space of spinning particles (spinning space) are analysed. Simple solutions of the homogeneous part of these equations are expressed in terms of Killing-Yano tensors. The general results are applied to the case of the four-dimensional euclidean Taub-NUT manifold.Comment: 10 pages, late

Generalized Taub-NUT metrics and Killing-Yano tensors

A necessary condition that a St\"ackel-Killing tensor of valence 2 be the contracted product of a Killing-Yano tensor of valence 2 with itself is re-derived for a Riemannian manifold. This condition is applied to the generalized Euclidean Taub-NUT metrics which admit a Kepler type symmetry. It is shown that in general the St\"ackel-Killing tensors involved in the Runge-Lenz vector cannot be expressed as a product of Killing-Yano tensors. The only exception is the original Taub-NUT metric.Comment: 14 pages, LaTeX. Final version to appear in J.Phys.A:Math.Ge

Nonholonomic Ricci Flows and Running Cosmological Constant: I. 4D Taub-NUT Metrics

In this work we construct and analyze exact solutions describing Ricci flows and nonholonomic deformations of four dimensional (4D) Taub-NUT spacetimes. It is outlined a new geometric techniques of constructing Ricci flow solutions. Some conceptual issues on spacetimes provided with generic off-diagonal metrics and associated nonlinear connection structures are analyzed. The limit from gravity/Ricci flow models with nontrivial torsion to configurations with the Levi-Civita connection is allowed in some specific physical circumstances by constraining the class of integral varieties for the Einstein and Ricci flow equations.Comment: latex2e, final variant to be published in IJMP