.htaccess rewrite/redirect problem (case is changing)

I have a website (Apache 1.3.37 on Linux) which has four domains pointed to it (olddomain1.com, olddomain2.com, olddomain3.com and newdomain.com).  I am trying to modify the .htaccess file so that whenever someone browses to it using the old domain names they are (permanently) redirected to the same page but using the new domain name.  

For example when someone requests
      http://www.olddomain2.com/Cust/Index.html
they should be redirected (permanently) to
      http://www.newdomain.com/Cust/Index.html

This is what I have in the .htaccess file:

      Options All -Indexes +FollowSymLinks
      RewriteEngine on
      RewriteCond %{HTTP_HOST} ^www\.olddomain1\.com$ [NC,OR]
      RewriteCond %{HTTP_HOST} ^olddomain1\.com$ [NC,OR]
      RewriteCond %{HTTP_HOST} ^www\.olddomain2\.com$ [NC,OR]
      RewriteCond %{HTTP_HOST} ^olddomain2\.com$ [NC,OR]
      RewriteCond %{HTTP_HOST} ^www\.olddomain3\.com$ [NC,OR]
      RewriteCond %{HTTP_HOST} ^olddomain3\.com$ [NC,OR]
      RewriteRule (.*) http://www.newdomain.com/$1 [R=301,L]

My problem is, when I browse to a web page the domain name replacement happens but the path and file name of the page is transformed into lowercase.  Naturally this doesn't work as the web server is case sensitive.

For example, when I browse to:
      http://www.olddomain2.com/Cust/Index.html
I receive:
      http://www.newdomain.com/cust/index.html

Could someone please help me to correct the .htaccess file so that I have permanent redirections from the old domain names but preserves the case of the path and filename of the web pages so that they display?

Thank you for your time.