Rich snippet with Woocommerce

Hi all,

I have an issue when testing a product page on https://www.google.com/webmasters/tools/richsnippets

I got the following errors :

In the first tab (hatom feed)

Erreur : Missing required field “updated”.
Erreur : Missing required hCard “author”.

In tab “item” where the description is a review by customer

Erreur : Incomplete microdata with schema.org.

So my rich snippet preview is without STARS/PRICE/NOTE/NB OF REVIEWS

How come?

Tks very much for any help !