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The spatial distribution of exoplanets in the Galaxy is important for ourunderstanding of planet formation and evolution. We aim to determine thespatial gradients of exoplanet occurrence in the Solar neighbourhood and in thevicinity of open clusters. We combined Kepler and Gaia DR2 data for thispurpose, splitting the volume sampled by the Kepler mission into certainspatial bins. We determined an uncorrected and bias-corrected exoplanetfrequency and metallicity for each bin. There is a clear drop in theuncorrected exoplanet frequency with distance for F-type stars, a decline withincreasing distance along the Galactic longitude l=90 deg, and a drop withheight above the Galactic plane. We find that the metallicity behaviour cannotbe the reason for the drop of the exoplanet frequency around F stars withincreasing distance. We argue that the above-mentioned gradients of uncorrectedexoplanet frequency result from a single bias of undetected smaller planetsaround fainter stars. When we correct for observational biases, most of thesegradients in exoplanet frequency become statistically insignificant. Only aslight decline of the planet occurrence with distance for F stars remainssignificant at the 3 sigma level. Apart from that, the spatial distribution ofexoplanets in the Kepler field of view is compatible with a homogeneous one. Atthe same time, we do not find a significant change in the exoplanet frequencywith increasing distance from open clusters. As a byproduct, we identified sixexoplanet host star candidates that are members of open clusters. Four of themare in the NGC 6811 (KIC 9655005, KIC 9533489, Kepler-66, Kepler-67) and twobelong to NGC 6866 (KIC 8396288, KIC 8331612). Two out of the six had alreadybeen known to be cluster members.

Spatial distribution of exoplanet candidates based on Kepler and $Gaia$ data