public T OpenDataset<T>( 
   string name
)
where T: Dataset

public async Task OpenTerrain()
{
  try
  {
    await ArcGIS.Desktop.Framework.Threading.Tasks.QueuedTask.Run(() =>
    {
      string path = @"d:\Data\Terrain\filegdb_Containing_A_Terrain.gdb";
      var fileConnection = new FileGeodatabaseConnectionPath(new Uri(path));

      using (Geodatabase dataStore = new Geodatabase(fileConnection))
      {
        string dsName = "nameOfTerrain";

        using (var dataset = dataStore.OpenDataset<ArcGIS.Core.Data.Analyst3D.Terrain>(dsName))
        {
        }
      }
    });
  }
  catch (GeodatabaseNotFoundOrOpenedException exception)
  {
    // Handle Exception.
  }
}

public async Task OpeningDatasetsFromGeodatabase()
{
    await ArcGIS.Desktop.Framework.Threading.Tasks.QueuedTask.Run(() =>
    {
        using (Geodatabase geodatabase = new Geodatabase(new DatabaseConnectionFile(new Uri("path\\to\\sde\\file\\sdefile.sde"))))
        {
            using (Table table = geodatabase.OpenDataset<Table>("LocalGovernment.GDB.EmployeeInfo"))
            {
            }

            // Open a featureClass (within a feature dataset or outside a feature dataset).
            using (FeatureClass featureClass = geodatabase.OpenDataset<FeatureClass>("LocalGovernment.GDB.AddressPoint"))
            {
            }

            // You can open a FeatureClass as a Table which will give you a Table Reference.
            using (Table featureClassAsTable = geodatabase.OpenDataset<Table>("LocalGovernment.GDB.AddressPoint"))
            {
                // But it is really a FeatureClass object.
                FeatureClass featureClassOpenedAsTable = featureClassAsTable as FeatureClass;
            }

            // Open a FeatureDataset.
            using (FeatureDataset featureDataset = geodatabase.OpenDataset<FeatureDataset>("LocalGovernment.GDB.Address"))
            {
            }

            // Open a RelationsipClass.  Just as you can open a FeatureClass as a Table, you can also open an AttributedRelationshipClass as a RelationshipClass.
            using (RelationshipClass relationshipClass = geodatabase.OpenDataset<RelationshipClass>("LocalGovernment.GDB.AddressPointHasSiteAddresses"))
            {
            }
        }
    });
}

public bool IsTableVersioned(Geodatabase geodatabase, string tableName)
{
    using (Table table = geodatabase.OpenDataset<Table>(tableName))
    {
        // Check table version type
        RegistrationType registrationType = table.GetRegistrationType();
        if (registrationType == RegistrationType.Versioned)
        {
            return true;
        }
    }
    return false;
}

// 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");