The paper surveys open problems and questions related to different aspects of integrable
systems with finitely many degrees of freedom. Many of the open problems were suggested …

Differential invariants of Kundt spacetimes - IOPscience This site uses cookies. By continuing
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We develop a general theory for irreducible homogeneous spaces M= G/H, in relation to the
nullity distribution ν of their curvature tensor. We construct natural invariant (different and …

We find new conditions that the existence of nullity of the curvature tensor of an irreducible
homogeneous space $ M= G/H $ imposes on the Lie algebra $\mathfrak g $ of $ G $ and on …

We devise an algorithm which allows one to count the number of Killing vectors for a
Lorentzian manifold of dimension 3. Our algorithm relies on the principal traces of powers of …

A three-dimensional Riemannian manifold has locally 6, 4, 3, 2, 1 or no independent Killing
vectors. We present an explicit algorithm for the computing dimension of infinitesimal …

We compute analytically differential curvature invariants for accelerating, rotating and
charged black holes with a cosmological constant Λ. Specifically, we compute novel closed …

We compute the full isometry group of any left-invariant metric on a simply connected, non-
unimodular Lie group of dimension three. As an application, we determine the index of …

We determine the index of symmetry of 3-dimensional unimodular Lie groups with a left-
invariant metric. In particular, we prove that every 3-dimensional unimodular Lie group …

Abstract Let π: E → M π: E→ M be a vector bundle over a simply connected manifold, ∇∇ a
linear connection in π π, and σ: U → E σ: U→ E a ∇∇-parallel section of π π defined on a …