I would declare an empty String variable like this:
string myString = string.Empty;
Is there an equivalent for a \'DateTime\' variable
A string is a sequence of characters. So it makes sense to have an empty string, which is just an empty sequence of characters.
But DateTime is just a single value, so it's doesn't make sense to talk about an “empty” DateTime.
If you want to represent the concept of “no value”, that's represented as null in .Net. And if you want to use that with value types, you need to explicitly make them nullable. That means either using Nullable, or the equivalent DateTime?.
DateTime (just like all value types) also has a default value, that's assigned to uninitialized fields and you can also get it by new DateTime() or default(DateTime). But you probably don't want to use it, since it represents valid date: 1.1.0001 0:00:00.