public T GetDefinition<T>( 
   string name
)
where T: Definition

public async Task ObtainingDefinitionFromGeodatabase()
{
    await ArcGIS.Desktop.Framework.Threading.Tasks.QueuedTask.Run(() =>
    {
        using (Geodatabase geodatabase = new Geodatabase(new DatabaseConnectionFile(new Uri("path\\to\\sde\\file\\sdefile.sde"))))
        {
            // Remember that for Enterprise databases you have to qualify your dataset names with the DatabaseName and UserName.
            TableDefinition enterpriseTableDefinition = geodatabase.GetDefinition<TableDefinition>("LocalGovernment.GDB.CitizenContactInfo");

            // It does not matter if the dataset is within a FeatureDataset or not.
            FeatureClassDefinition featureClassDefinition = geodatabase.GetDefinition<FeatureClassDefinition>("LocalGovernment.GDB.FireStation");

            // GetDefinition For a RelationshipClass.
            RelationshipClassDefinition relationshipClassDefinition = geodatabase.GetDefinition<RelationshipClassDefinition>("LocalGovernment.GDB.AddressPointHasSiteAddresses");

            // GetDefinition For a FeatureDataset.
            FeatureDatasetDefinition featureDatasetDefinition = geodatabase.GetDefinition<FeatureDatasetDefinition>("LocalGovernment.GDB.Address");
        }
    });
}

// Must be called within QueuedTask.Run9)
public bool TableExists(Geodatabase geodatabase, string tableName)
{
    try
    {
        TableDefinition tableDefinition = geodatabase.GetDefinition<TableDefinition>(tableName);
        tableDefinition.Dispose();
        return true;
    }
    catch
    {
        // GetDefinition throws an exception if the definition doesn't exist
        return false;
    }
}

// Must be called within QueuedTask.Run()
public bool FeatureClassExists(Geodatabase geodatabase, string featureClassName)
{
    try
    {
        FeatureClassDefinition featureClassDefinition = geodatabase.GetDefinition<FeatureClassDefinition>(featureClassName);
        featureClassDefinition.Dispose();
        return true;
    }
    catch
    {
        // GetDefinition throws an exception if the definition doesn't exist
        return false;
    }
}