As others have mentioned, you seem to be confusing resolution and frame rate. There are variable resolution systems for things like VR for foviated rendering (where the area being looked at is rendered in higher resolution than the surrounding areas) and there are also some large format displays where the resolution of the overall visual display may not be consistent, but you aren't talking about either of these situations.
For a conventional display viewed by multiple people, you aren't going to be able to meaningfully change the resolution throughout the video without it being pretty jarring. What you are talking about instead is the idea of varying the frame rate (how often the image updates) or group of pictures compression (where surrounding frames are described in terms of their differences from another frame rather than describing the full image for every frame.
In fact, virtually all modern video codecs use the latter of these two. Groups of pictures have been used in pretty much every video format since the MPEG-2 and the DVD (with some usage before as well). This compression technique is why we can get such incredible compression with so little quality loss.
To put it in perspective, an individual raw frame of 4k video from my Ursa Mini digital cinema camera is 10MB. At 24 frames a second, that's 240MB/sec (bytes, not bits), yet Netflix can give a reasonable quality 4k video feed at only 15Mb/sec (bits, not bytes), that's 1/128th of the data involved in the RAW video with relatively minimal visible difference (and that's before calculating the color information which would actually nearly triple the overall data rate making it less than 1/300th of the uncompressed video).
Simply put, our video compression options available already are staggering using just the latter of these options and will tend to work even better on low motion video where very little changes between frames. 2 pass encoding will give the best result as it will determine the amount of change between frames in the first pass and then optimize the data storage on the second.
Variable frame rate is an option you can pursue to further lower the bandwidth requirements if large portions truly do not need to change at all, but such encoders are more complicated, less commonly available and don't play back quite as reliably across devices. Overall, I'd try seeing what you can get with careful tweaking of modern h.264 or h.265 algorithms with fairly long GOP settings (long key frame intervals).