Let be a presymplectic groupoid. In this paper we characterize the infinitesimal counter part of the tangent presymplectic groupoid of higher order, where is the tangent groupoid of higher order and is the complete lift of higher order of presymplectic form .
A Theorem is proved that gives intrinsic necessary and sufficient conditions for the integrability of a zero-deformable field of endomorphisms. The Theorem is proved by reducing to a special case in which the endomorphism field is nilpotent. Many arguments used in the derivation of similar results are simplified, principally by means of using quotient rather than subspace constructions.
We study the intrinsic torsion of almost quaternion-Hermitian manifolds via the exterior algebra. In particular, we show how it is determined by particular three-forms formed from simple combinations of the exterior derivatives of the local Kähler forms. This gives a practical method to compute the intrinsic torsion and is applied in a number of examples. In addition we find simple characterisations of HKT and QKT geometries entirely in the exterior algebra and compute how the intrinsic torsion...
We consider the level set formulation of the inverse mean curvature flow. We establish a connection to the problem of -harmonic functions and give a new proof for the existence of weak solutions.