The closest technology in DirectX that would provide a basic infrastructure for "Ink rendering" would be Direct2D. This is probably what "InkManager" is using internally, at least for the drawing part. There is no "handwriting recognition" in Direct2D. But as Direct2D is a low level API, you will have to manage lots of details.
There are dozens of samples in SharpDX with Direct2D (either samples on Desktop - where the drawing part is still valid on WinRT, or plain WinRT), but you will not have a direct "Ink" samples, so you will have to dig into this yourself.
Also, the only source of information for Direct2D is msdn. There is no book and very view tutorials about this API.