Generalised contact geometry as reduced generalised Complex geometry

Generalised Complex Geometry and the Planck Cone

Complex geometry and symplectic geometry are mirrors in string theory. The recently developed generalised complex geometry interpolates between the two of them. On the other hand, the classical and quantum mechanics of a finite number of degrees of freedom are respectively described by a symplectic structure and a complex structure on classical phase space. In this letter we analyse the role pl...

Generalised Complex Geometry in Thermodynamical Fluctuation Theory

We present a brief overview of some key concepts in the theory of generalized complex manifolds. This new geometry interpolates, so to speak, between symplectic geometry and complex geometry. As such it provides an ideal framework to analyze thermodynamical fluctuation theory in the presence of gravitational fields. To illustrate the usefulness of generalized complex geometry, we examine a simp...

Ed(d) × R Generalised Geometry

Synthetic Geometry and Generalised Functions

We review some aspects of the geometry of length spaces and metric spaces, in particular Alexandrov spaces with curvature bounded below and/or above. We then point out some possible directions of research to explore connections between the synthetic approach to Riemannian geometry and some aspects of the approach to non-smooth differential geometry through generalised functions. AMS Mathematics...

Generalised Geometry for M-Theory

Generalised geometry studies structures on a d-dimensional manifold with a metric and 2-form gauge field on which there is a natural action of the group SO(d, d). This is generalised to d-dimensional manifolds with a metric and 3-form gauge field on which there is a natural action of the group Ed. This provides a framework for the discussion of M-theory solutions with flux. A different generali...