We describe a novel twistorial construction of the asymptotic Bondi-Metzner-Sachs (BMS) symmetries at null infinity for asymptotically flat spacetimes. define BMS twistors as spinor solutions to some set components usual spacetime twistor equation restricted infinity. The space is infinite dimensional. show that given two twistors, their symmetric tensor product can be used generate (complex) v...

We revisit the symmetry structure of integrable PDEs, looking at specific example KdV equation. identify 4 nonlocal symmetries depending on a parameter, which we call generating symmetries. explain that since these are symmetries, their commutator algebra is not uniquely determined, and present three possibilities for algebra. In first version, 3 commute; this shows it possible to add further (...

We construct explicit examples of quaternion-Kähler and hypercomplex structures on bundles over hyperKähler manifolds. study the infinitesimal symmetries these associated Galicki–Lawson moment map. By performing QK reduction we produce several metrics. Moreover are led to a new proof hyperKähler/quaternion-Kähler type correspondence. also give other Einstein metrics balanced Hermitian bundles.

Let  be an n-dimensional Riemannian manifold, and  be its tangent bundle with the lift metric. Then every infinitesimal fiber-preserving conformal transformation  induces an infinitesimal homothetic transformation on .  Furthermore,  the correspondence   gives a homomorphism of the Lie algebra of infinitesimal fiber-preserving conformal transformations on  onto the Lie algebra of infinitesimal ...

Using the S.Lie’s infinitesimal approach we establish the connection between integrability of a one-parameter family of the Riccati equations and the stationary KdV hierarchy. In this paper we will suggest a method for integrating a one-parameter family of the Riccati equations ux + u 2 = f(x, λ) (1) based on their Lie symmetries. Here f(x, λ) = λ + λVn−1(x) + · · ·+ λV1(x) + V0(x) and λ is an ...

In this paper, we introduce a natural classification of bar and joint frameworks that possess symmetry. This classification establishes the mathematical foundation for extending a variety of results in rigidity, as well as infinitesimal or static rigidity, to frameworks that are realized with certain symmetries and whose joints may or may not be embedded injectively in the space. In particular,...

The paper addresses the question whether in four spacetime dimensions, besides standard supergravity theories, field theories exist whose symmetries include local translations and supersymmetries generated by transformations commutators contain infinitesimal translations. It is shown that, up to redefinitions, there a unique class of such supersymmetric satisfying specified prerequisites which ...