Rsync copy fails ("no such file or directory")

The error comes from the fact that there is no /public_html/abc directory on the remote system.

According to comments, the source directory is actually located in the user's home directory, not at the path /public_html.

Therefore:

rsync -avzP [email protected]:public_html/abc/ /www/abc

Here, we access public_html/abc in the user's home directory rather than in the root of the filesystem.

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The warning stdin: is not a tty comes from the fact that your shell's startup file for interactive shells is being called on the remote host (your ~/.bashrc file, if you are using bash), and you are doing something in it that requires a terminal.

You may edit the shell startup file on the remote machine and insert the following close to the top:

[ ! -t 0 ] && return

This would stop the execution of e.g. ~/.bashrc at that point for all shell sessions whose standard input streams are not attached to a terminal.

You need to add the connection details, eg. for SSH use --rsh=ssh.

Try:

rsync -avzP --rsh=ssh [email protected]:/public_html/abc/ /www/abc

And make sure the paths are correct. Are these paths absolute or relative: /public_html/abc/, /www/abc?