  In a system of heterogeneous (Abelian) Kuramoto oscillators with random or
`frustrated' interactions, transitions from states of incoherence to partial
synchronization were observed. These so-called volcano transitions are
characterized by a change in the shape of a local field distribution and were
discussed in connection with an oscillator glass. In this paper, we consider a
different class of oscillators, namely a system of (non-Abelian) SU(2)-Lohe
oscillators that can also be defined on the 3-sphere, i.e., an oscillator is
generalized to be defined as a unit vector in 4D Euclidean space. We
demonstrate that such higher-dimensional Kuramoto models with reciprocal and
nonreciprocal random interactions represented by a low-rank matrix exhibit a
volcano transition as well. We determine the critical coupling strength at
which a volcano-like transition occurs, employing an Ott-Antonsen ansatz.
Numerical simulations provide additional validations of our analytical findings
and reveal the differences in observable collective dynamics prior to and
following the transition. Furthermore, we show that a system of unit 3-vector
oscillators on the 2-sphere does not possess a volcano transition.
