Surface holonomy and gauge 2-group

Just as point objects are parallel transported along curves, giving holonomies, string-like objects are parallel transported along surfaces, giving surface holonomies. Composition of these surfaces correspond to products in a category theoretic generalization of the gauge group, called a 2-group. I consider two different ways of constructing surface holonomies, one by using a pair of one and two form connections, and another by using a pair of one-form connections. Both procedures result in the structure of a 2-group.Comment: 8pp, RevTeX4, Submitted upon invitation to IJGMM

Parallel spinors and holonomy groups

In this paper we complete the classification of spin manifolds admitting parallel spinors, in terms of the Riemannian holonomy groups. More precisely, we show that on a given n-dimensional Riemannian manifold, spin structures with parallel spinors are in one to one correspondence with lifts to Spin_n of the Riemannian holonomy group, with fixed points on the spin representation space. In particular, we obtain the first examples of compact manifolds with two different spin structures carrying parallel spinors.Comment: 10 pages, LaTeX2

Electronic system for high power load control

Parallel current paths are divided into two groups, with control devices in the current paths of one group each having a current limiting resistor, and the control devices in the other group each having no limiting resistor, so that when the control devices of the second group are turned fully on, a short circuit is achieved by the arrangement of parallel current paths. Separate but coordinated control signals are provided to turn on the control devices of the first group and increase their conduction toward saturation as a function of control input, and when fully on, or shortly before, to turn on the control devices of the second group and increase their conduction toward saturation as a function of the control input as that input continues to increase. Electronic means may be used to generate signals. The system may be used for 1-V characteristic measurements of solar arrays as well as for other load control purposes

Almost Hermitian 6-Manifolds Revisited

A Theorem of Kirichenko states that the torsion 3-form of the characteristic connection of a nearly K\"ahler manifold is parallel. On the other side, any almost hermitian manifold of type $\mathrm{G}_1$ admits a unique connection with totally skew symmetric torsion. In dimension six, we generalize Kirichenko's Theorem and we describe almost hermitian $\mathrm{G}_1$-manifolds with parallel torsion form. In particular, among them there are only two types of $\mathcal{W}_3$-manifolds with a non-abelian holonomy group, namely twistor spaces of 4-dimensional self-dual Einstein manifolds and the invariant hermitian structure on the Lie group \mathrm{SL}(2, \C). Moreover, we classify all naturally reductive hermitian $\mathcal{W}_3$-manifolds with small isotropy group of the characteristic torsion.Comment: 26 pages, revised versio