Generalizing eleven-dimensional supergravity

We develop a procedure to reproduce the ten-dimensional generalized supergravity equations from T-duality covariant equations, that facilitates generalization U-duality formulations of eleven-dimensional supergravity. The latter leads modification with terms contain rank-2 tensor field $J^{mn}$ which is analog non-unimodularity Killing vector $I^m$ in ten dimensions.