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... groups in 11-dimensional supergravity has been discussed over a period of years by amongst others [9, 10, 11, 12]. Recent work studying the idea of curvatures in generalized geometry has appeared in =-=[13, 14]-=- and for the Heterotic string in [15]. 2 Generalized Metrics and their dynamics Generalized metrics are metrics on an extended tangent space. In the initial work of Hitchin corresponding to string the...

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...rtant independent work [18,19]. The precise relation to the formulation in terms of a generalized metric is by now well-understood both at the level of the symmetry transformations [4] and the action =-=[6]-=-. Siegel’s formalism as presented in [18] is already adapted to include the abelian subsector of the heterotic theory. Using the recent results of [6], it is straightforward to verify the equivalence ...

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...irst formalism was developed some time ago by Siegel [5]. It is a frame formalism that is the analogue of the vielbein formulation of general relativity and has been related to double field theory in =-=[8]-=-. The second formulation is a metric-like formalism with Christoffel-type connections. As in general relativity, the second formulation is related to the first by a ‘vielbein postulate’ [8, 16]. It ha...

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... A natural question given generalized geometry defined by a metric is how does one construct a connection and curvature. The attempts to construct these ideas in generalized geometry are described in =-=[28, 29, 30, 10]-=-. This equivalence (and subsequent neglect of boundary terms) was described for the doubled string in [27], the extended heterotic string in [31] and in M–theory in [19, 20, 21]. There are two possibi...

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...of an appropriate connection à la general relativity. In fact a frame like formulation with a local Gl(d)× Gl(d) symmetry dates back to the pioneering work of Siegel [9, 10]. A number of recent works =-=[132, 133, 134, 135, 136, 137, 138]-=- have further developed the geometrical concepts predominantly in a Christoffel-like approach. The basic idea is to introduce an appropriate connection to covariantise all derivatives. That is to say,...

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...mposing a 1The analogy with Riemannian geometry is not complete: there is no contraction of RMN that gives R. 3 vielbein postulate that relates the Christoffel-like connections to the spin-connection =-=[7]-=-. This will be briefly explained in the appendix. We find it simpler and more illuminating, however, to present the metric-like formalism in a self-contained fashion. A closely related formulation has...