Linear connections on Courant algebroids are a natural extension of vector bundle connections. However, it is not straightforward to find suitable definitions of torsion and curvature operators. After a brief introduction to the theory of Courant algebroids and linear connections, such definitions are discussed. Interestingly, they provide a surprisingly natural desctription of certain equations of motion coming from supergravity and string theory. This encourages a further study of these geometrical structures.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/3946