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");