You might Krystof Kieslowski. He only did a few feature films, but they are very moving, unconventional, and have a lot of depth. I often place Kieslowski and Tarkovsky on the same pedestal. Tarkovsky is my favorite, but Kieslowski follows closely.
As for another Russian who has a similar style to Tarkovsky but with a touch more narrative, check out Andrey Zvyagintsev. His films are definitely the offspring of the Russian Auteurs.
Re: Viewing films after Tarkovsky's films
As for another Russian who has a similar style to Tarkovsky but with a touch more narrative, check out Andrey Zvyagintsev. His films are definitely the offspring of the Russian Auteurs.