I think recurrence-id is not exposed by any property on the Event object.
You'll have to set it manually, adding custom header, using Event.AddCustomHeader method.
PdiHeader rid = new PdiHeader("RECURRENCE-ID","19960401");
rid.KeyParameters.Add(new KeyValues("VALUE", "DATE"));
theEvent.AddCustomHeader(rid);
PdiHeader rid = new PdiHeader("RECURRENCE-ID","19960120T120000Z");
rid.KeyParameters.Add(new KeyValues("RANGE", "THISANDFUTURE"));
theEvent.AddCustomHeader(rid);
You can use Event.GetHeader method, to retrieve this header:
PdiHeader rid = event.GetHeader("RECURRENCE-ID");
string thisandfuture = rid.GetKeyParameter("RANGE");
string value = rid.Value("RANGE")