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Serve HTTPS requests from subdomain

I need a single Wordpress installation to be available from both the main domain (www.example.com) via HTTP and a subdomain (secure.example.com) via HTTPS.

Of course i can just map the subdomain to the Wordpress folder in Nginx config. But will Wordpress be aware that it is called via HTTPS and change all links on the pages to HTTPS ?

Also, how i can i force certain pages to be automatically redirected to their HTTPS equivalent permalink (and then back again to HTTP) ?