Installing Zimbra Desktop on 64bit Linux
From Zimbra :: Wiki
This guide describes some "fixes" needed to run the Zimbra Desktop on a 64bit Linux desktop. Just remember that even if works, it's an out-of-scope fix, and you may not receive support running the Zimbra Desktop 32bit on a 64bit Linux.
Distro Specific Fixes
Install the following libs before execute the installation procedure:
yum install -y alsa-lib.i686 libstdc++.i686 xulrunner.i686 gtk2-engines.i686
Install the following ia32 "wrap" packages on the system:
aptitude install ia32-libs-gtk
Note: I've removed the "default-jre" because your system could be already Java enabled/configured.
Environment Variables and others