  The morphological study is crucial to investigate the connections between
active galactic nuclei (AGN) activities and the evolution of galaxies.
Substantial studies have found that radiative-mode AGNs primarily reside in
disk galaxies, questioning the merger-driven mechanism of AGN activities. In
this study, through S{\'e}rsic profile fitting and non-parametric morphological
parameter measurements, we investigated the morphology of host galaxies of 485
optical variability-selected low luminosity AGNs at $z\lesssim4.26$ in the
COSMOS field. We analyzed high-resolution images of the Hubble Space Telescope
to measure these morphological parameters. We only successfully measured the
morphological parameters for 76 objects and most AGN hosts ($\sim70\%$) were
visually compact point-like sources. We examined the obtained morphological
information as a function of redshift and compared them with literature data.
We found that these AGN host galaxies showed no clear morphological preference.
However, the merger rate increased with the higher hosts' SFRs and AGN
luminosity. Interestingly, we found ongoing star formation consistent with the
typical star forming populations in both elliptical and spiral galaxies while
these two types of galaxies were more symmetric than normal star forming
galaxies. These results suggested that optical variability-selected AGNs have}
higher probabilities to reside in elliptical galaxies than infrared-selected
AGNs (IR-AGNs), whose host galaxies had a strong disk-dominance, and supported
recent studies that the AGN feedback could enhance star forming activities in
host galaxies.
