Title: Wind Riemannian spaceforms and Randers metrics of constant flag curvature,
Abstract: Recently, wind Riemannian structures (WRS) have been introduced as a
generalization of Randers and Kropina metrics. They are constructed from the
natural data for Zermelo navigation problem, namely, a Riemannian metric $g_R$
and a vector field $W$ (the wind), where, now, the restriction of mild wind
$g_R(W,W)<1$ is dropped.
Here, the models of WRS spaceforms of constant flag curvature are determined.
Indeed, the celebrated classification of Randers metrics of constant flag
curvature by Bao, Robles and Shen, extended to the Kropina case in the works by
Yoshikawa, Okubo and Sabau, can be used to obtain the local classification. For
the global one, a suitable result on completeness for WRS yields the complete
simply connected models. In particular, any of the local models in the Randers
classification does admit an extension to a unique model of wind Riemannian
structure, even if it cannot be extended as a complete Finslerian manifold.
Thus, WRS's emerge as the natural framework for the analysis of Randers
spaceforms and, prospectively, wind Finslerian structures would become
important for other global problems too. For the sake of completeness, a brief
overview about WRS (including a useful link with the conformal geometry of a
class of relativistic spacetimes) is also provided.