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;
  }
}