  For several transition disks (TDs), dark regions interpreted as shadows have
been observed in scattered light imaging and are hypothesized to originate from
misalignments between distinct disk regions. We aim to investigate the presence
of misalignments in TDs. We study the inner disk geometries of 20 well-known
transition disks with VLTI/GRAVITY observations and use complementary $^{12}$CO
and $^{13}$CO molecular line data from ALMA to derive the orientation of the
outer disk regions. We fit simple models to the GRAVITY data to derive the
inner disks inclination and position angles. The outer disk geometries were
derived from Keplerian fits to the ALMA velocity maps and compared to the inner
disk constraints. We also predicted the locations of shadows for significantly
misaligned systems. Our analysis reveals six disks to exhibit significant
misalignments between their inner and outer disks. The predicted shadow
positions agree well with the scattered light images of HD100453 and HD142527,
and we find supporting evidence for a shadow in the disk around CQ Tau. In the
other three targets for which we infer significantly misaligned disks, V1247
Ori, V1366 Ori, and RY Lup, we do not see any evident sign of shadows in the
scattered light images. The scattered light shadows observed in DoAr44,
HD135344B, and HD139614 are consistent with our observations, yet the
underlying morphology is likely too complex to be described by our models and
the accuracy achieved by our observations. Whereas we can derive precise
constraints on the potential shadow positions for well-resolved inner disks
around HAeBe stars, the statistical uncertainties for the marginally resolved
inner disks around the TTS of our sample make it difficult to extract
conclusive constraints for the presence of shadows in these systems.

Earth and Planetary Astrophysics;Solar and Stellar Astrophysics