public IReadOnlyList<string> GetFeatureClassNames()

public async Task GetTerrainDefinition()
{
  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 terrainDef = dataStore.GetDefinition<ArcGIS.Core.Data.Analyst3D.TerrainDefinition>(dsName))
        {
          // get the feature class names that are used in the terrain
          var fcNames = terrainDef.GetFeatureClassNames();
        }
      }
    });
  }
  catch (GeodatabaseNotFoundOrOpenedException exception)
  {
    // Handle Exception.
  }
}