Question

Edited: To better explain what i want.

We want to move our frontpage http://www.example.com, to a subpage http://www.example.com/sub-page.

So in order to keep our SEO ranking we need to write a 301 permanently moved. And we would like the sub-page URL to be displayed in the browser.
This should be displayed http://www.example.com/sub-page/

So the result will be if you try to enter http://www.example.com, your url will be rewritten to http://www.example.com/sub-page/ with a 301 redirect.

But every other page should not be redirected!
E.g. http://www.example.com/contact/ should still be the same.

And it should also take care of every variations of the root-domain.
With and without trailing slashes (example.com/ vs example.com)
With and without www (www.example.com vs example.com)

Answer 1

1. Enable mod_rewrite and .htaccess. 
2. Create and deploy your new home page as `/sub-page`
3. Then put this code in your .htaccess file under DOCUMENT_ROOT:

Options +FollowSymLinks -MultiViews
# Turn mod_rewrite on
RewriteEngine On
RewriteBase /

# reqest to example.com/ will be forwarded to example.com/sub-page
RewriteRule ^$ sub-page [L,R=301]