Hypercomplex structures on Courant algebroids
نویسندگان
چکیده
منابع مشابه
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 ...
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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...
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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...
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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: Comptes Rendus Mathematique
سال: 2009
ISSN: 1631-073X
DOI: 10.1016/j.crma.2009.02.020