Generalized Connections, Spinors, and Integrability of Generalized Structures on Courant Algebroids

Hypercomplex Structures on Courant Algebroids

In this note, we prove the equivalence of two characterizations of hypercomplex structures on Courant algebroids, one in terms of Nijenhuis concomitants and the other in terms of (almost) torsionfree connections for which each of the three complex structures is parallel. A Courant algebroid [4] consists of a vector bundle π : E → M , a nondegenerate symmetric pairing 〈, 〉 on the fibers of π, a ...

Elliptic Involutive Structures and Generalized Higgs Algebroids

ELLIPTIC INVOLUTIVE STRUCTURES AND GENERALIZED HIGGS ALGEBROIDS Eric O. Korman Jonathan Block We study the module theory of two types of Lie algebroids: elliptic involutive structures (EIS) (which are equivalent to transversely holomorphic foliations) and what we call twisted generalized Higgs algebroids (TGHA). Generalizing the wellknown results in the extremal cases of flat vector bundles and...

On Regular Courant Algebroids

For any regular Courant algebroid, we construct a characteristic class à la Chern-Weil. This intrinsic invariant of the Courant algebroid is a degree-3 class in its naive cohomology. When the Courant algebroid is exact, it reduces to the Ševera class (in H DR(M)). On the other hand, when the Courant algebroid is a quadratic Lie algebra g, it coincides with the class of the Cartan 3-form (in H(g...

On Generalized Weak Structures

Avila and Molina [1] introduced the notion of generalized weak structures which naturally generalize minimal structures, generalized topologies and weak structures and the structures α(g),π(g),σ(g) and β(g). This work is a further investigation of generalized weak structures due to Avila and Molina. Further we introduce the structures ro(g) and rc(g) and study the properties of the structures r...

Properties of Generalized Berwald Connections