Conformal properties of harmonic spinors and lightlike geodesics in signature (1, 1)

Conformal properties of harmoni spinors and lightlike

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This article provides us with a unifying classification of the conformal infinitesimal symmetries of non-relativistic Newton-Cartan spacetime. The Lie algebras of non-relativistic conformal transformations are introduced via the Galilei structure. They form a family of infinite-dimensional Lie algebras labeled by a rational “dynamical exponent”, z. The Schrödinger-Virasoro algebra of Henkel et ...

Fermat Principle in Finsler Spacetimes

It is shown that, on a manifold with a Finsler metric of Lorentzian signature, the lightlike geodesics satisfy the following variational principle. Among all lightlike curves from a point q (emission event) to a timelike curve γ (worldline of receiver), the lightlike geodesics make the arrival time stationary. Here “arrival time” refers to a parametrization of the timelike curve γ. This variati...

Non–trivial Harmonic Spinors on Generic Algebraic Surfaces

For every closed Riemannian spin manifold its Dirac operator is a selfadjoint linear elliptic operator acting on sections of the spinor bundle. Hitchin [3] proved that the dimension of its kernel, the space of harmonic spinors, only depends on the conformal class of the Riemannian metric, and that it varies with the conformal class. However, the variation is not understood. Investigating this v...

Closed conformal vector fields on pseudo-Riemannian manifolds

∇XV = λX for every vector field X. (1.2) Here ∇ denotes the Levi-Civita connection of g. We call vector fields satisfying (1.2) closed conformal vector fields. They appear in the work of Fialkow [3] about conformal geodesics, in the works of Yano [7–11] about concircular geometry in Riemannian manifolds, and in the works of Tashiro [6], Kerbrat [4], Kühnel and Rademacher [5], and many other aut...