TY - JOUR
T1 - On Curvature and Torsion in Courant Algebroids
AU - Aschieri, Paolo
AU - Bonechi, Francesco
AU - Deser, Andreas
N1 - Publisher Copyright:
© 2021, Springer Nature Switzerland AG.
PY - 2021/7
Y1 - 2021/7
N2 - We study the graded geometric point of view of curvature and torsion of Q-manifolds (differential graded manifolds). In particular, we get a natural graded geometric definition of Courant algebroid curvature and torsion, which correctly restrict to Dirac structures. Depending on an auxiliary affine connection K, we introduce the K-curvature and K-torsion of a Courant algebroid connection. These are conventional tensors on the body. Finally, we compute their Ricci and scalar curvature.
AB - We study the graded geometric point of view of curvature and torsion of Q-manifolds (differential graded manifolds). In particular, we get a natural graded geometric definition of Courant algebroid curvature and torsion, which correctly restrict to Dirac structures. Depending on an auxiliary affine connection K, we introduce the K-curvature and K-torsion of a Courant algebroid connection. These are conventional tensors on the body. Finally, we compute their Ricci and scalar curvature.
UR - http://www.scopus.com/inward/record.url?scp=85101112969&partnerID=8YFLogxK
U2 - 10.1007/s00023-021-01024-5
DO - 10.1007/s00023-021-01024-5
M3 - Article
SN - 1424-0637
VL - 22
SP - 2475
EP - 2496
JO - Annales Henri Poincare
JF - Annales Henri Poincare
IS - 7
ER -