Hi Marie.
Thanks for the question, but this isn’t an existing feature.
If a plugin like Jetpack’s Sharing feature adds share buttons on Event Single pages, each social site should pick up the event details and it should turn out ok (maybe even exactly what you’re looking for).
If you don’t feel this provides you an acceptable solution, you may want to share your idea at our plugins’ UserVoice page.
This allows others who are interested in that feature to easily voice their support. We frequently review suggestions there to find out which ones are popular, then we implement as many of them as we can.
Once you post it (or find an existing one to vote for), feel free to link to it from here in case anyone comes across this forum thread in the future.