Gnome-extension-webdav-ical is a project mainly written in Python, based on the GPL-3.0 license.
Synchronize Webdav+iCal calendars with gnome3 calendar
This is an extension for gnome3 which adds support for iCal calendars hosted on WebDAV. This should be able to support e.g. Zimbra and possibly Google (haven't tested that yet).
For now it's basically a proof of concept and works for me.
This is a combination of two existing github projects:
https://github.com/sochotnicky/pywebcal (Python module to simplify access to WebDAV calendars (Zimbra/Google Calendar etc.)) https://github.com/jnns/gnome-shell-google-calendar (An attempt to integrate google calendar into gnome-shell.)
You'll need to install pywebcal and it's requirements for this to work. (see https://github.com/sochotnicky/pywebcal)
Modify the script and change the 3 config variables in gnome-extension-webdav-ical.py and run the script.
It has to be running in the background and will fetch the updates when needed and supports some form of caching. I added it to the Startup Programs using gnome-session-properties.