  Temporal knowledge graphs represent temporal facts $(s,p,o,\tau)$ relating a
subject $s$ and an object $o$ via a relation label $p$ at time $\tau$, where
$\tau$ could be a time point or time interval. Temporal knowledge graphs may
exhibit static temporal patterns at distinct points in time and dynamic
temporal patterns between different timestamps. In order to learn a rich set of
static and dynamic temporal patterns and apply them for inference, several
embedding approaches have been suggested in the literature. However, as most of
them resort to single underlying embedding spaces, their capability to model
all kinds of temporal patterns was severely limited by having to adhere to the
geometric property of their one embedding space. We lift this limitation by an
embedding approach that maps temporal facts into a product space of several
heterogeneous geometric subspaces with distinct geometric properties, i.e.\
Complex, Dual, and Split-complex spaces. In addition, we propose a
temporal-geometric attention mechanism to integrate information from different
geometric subspaces conveniently according to the captured relational and
temporal information. Experimental results on standard temporal benchmark
datasets favorably evaluate our approach against state-of-the-art models.
