public FileGeodatabaseConnectionPath( 
   Uri path
)

public async Task OpenFileGDB()
{
  try
  {
    await ArcGIS.Desktop.Framework.Threading.Tasks.QueuedTask.Run(() =>
    {
      // Opens a file geodatabase. This will open the geodatabase if the folder exists and contains a valid geodatabase.
      using (
        Geodatabase geodatabase =
          new Geodatabase(new FileGeodatabaseConnectionPath(new Uri(@"C:\Data\LocalGovernment.gdb"))))
      {
        // Use the geodatabase.
      }
    });
  }
  catch (GeodatabaseNotFoundOrOpenedException exception)
  {
    // Handle Exception.
  }

}

// Create a FileGeodatabaseConnectionPath using the path to the gdb. Note: This can be a path to a .sde file.
FileGeodatabaseConnectionPath geodatabaseConnectionPath = new FileGeodatabaseConnectionPath(new Uri(@"C:\Temp\rasters.gdb"));
// Create a new Geodatabase object using the FileGeodatabaseConnectionPath.
Geodatabase geodatabase = new Geodatabase(geodatabaseConnectionPath);
// Open the raster dataset.
RasterDataset gdbRasterDataset = geodatabase.OpenDataset<RasterDataset>("sample");