There is no built-in equivalent (as far as I know).
The easiest way from the insert mode is to use Ctrl - O D.
If you want to match this with something easier to remember, you might want to create an insert-display mode that allows you to use normal D mode to delete characters under the cursor to the end of the line:
:inoremap <Leader>k <CO>D
Assuming that <Leader> is the default value \ , you should type \ k in insert mode, referring to the mapping.
Insert insert combinations are not without their flaws, as Kent points out in the comments, but have their own capabilities.
Ctrl - k is used to enter digraphs in Wim. I would suggest that you are not trying to redisplay this, although this is possible using the technique above.
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