how to convert datetime to short date?

You must call .ToString() method with that format that you want. In your example it will be like this.

DateTime date=DateTime.Now;
var shortDate=date.ToString("yyyy-MM-dd");

Or if you want to keep DateTime type, you must call .Date property of DateTime

DateTime date=DateTime.Now;
var shortDate=date.Date;

From MSDN

A new object with the same date as this instance, and the time value set to 12:00:00 midnight (00:00:00).

DateTime dateToDisplay = new DateTime(2014, 11, 03, 42, 50);
String shortDateTime = dateToDisplay.ToShortDateString();

Then you can convert this shortDateTime to datetime like this

DateTime shortDate = Convert.ToDateTime(shortDateTime);

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