منابع مشابه
Transitive Courant algebroids
We express any Courant algebroid bracket by means of a metric connection, and construct a Courant algebroid structure on any orthogonal, Whitney sum E⊕C where E is a given Courant algebroid and C is a flat, pseudo-Euclidean vector bundle. Then, we establish the general expression of the bracket of a transitive Courant algebroid, that is, a Courant algebroid with a surjective anchor, and describ...
متن کاملOn 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...
متن کاملHypercomplex 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 ...
متن کاملCourant Algebroids from Categorified Symplectic Geometry
In categorified symplectic geometry, one studies the categorified algebraic and geometric structures that naturally arise on manifolds equipped with a closed nondegenerate (n + 1)-form. The case relevant to classical string theory is when n = 2 and is called ‘2-plectic geometry’. Just as the Poisson bracket makes the smooth functions on a symplectic manifold into a Lie algebra, there is a Lie 2...
متن کاملCohomology of Courant algebroids with split base
In this paper we study the cohomology H• st (E) of a Courant algebroid E. We prove that if E is transitive, H• st (E) coincides with the naive cohomology H• naive (E) of E as conjectured by Stiénon and Xu [SX08]. For general Courant algebroids E we define a spectral sequence converging to H• st (E). If E is with split base, we prove that there exists a natural transgression homomorphism T3 (wit...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2005
ISSN: 0161-1712,1687-0425
DOI: 10.1155/ijmms.2005.1737