Which whitespace character? The empty string is pretty unambiguous – it’s a sequence of 0 characters. However, " ", "\t" and "\n" are all strings containing a single character which is characterized as whitespace.
If you just mean a space, use a space. If you mean some other whitespace character, there may well be a custom escape sequence for it (e.g. "\t" for tab) or you can use a Unicode escape sequence ("\uxxxx"). I would discourage you from including non-ASCII characters in your source code, particularly whitespace ones.
EDIT: Now that you’ve explained what you want to do (which should have been in your question to start with) you’d be better off using Regex.Split with a regular expression of \s which represents whitespace:
Regex regex = new Regex(@"\s");
string[] bits = regex.Split(text.ToLower());
See the Regex Character Classes documentation for more information on other character classes.