When you sync your Google account with your iPhone, it only adds the main calendar to the calendar application on your iDevice. Follow these instructions to get your additional calendars added to your iDevice.
Select Calendars to Sync
- Check the box next to the calendars you would like to sync to your iPhone.
- Click "Save."
Open Your Calendar App
You should now see multiple calendars listed under your account instead of just the primary one you had before.
If you don't, hit refresh button in the bottom left corner or just give it 5-10 minutes to pull in your new calendars. If the calendars still do not show up, go to your settings app and remove your Gmail Account and add it again.
Once you see your shared calendars, check the ones you want to view by default in the calendar app.