public sealed class TerrainDefinition : ArcGIS.Core.Data.Definition, System.IDisposable  

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.
  }
}

//Must be on the QueuedTask.Run()

Envelope extent;
SpatialReference sr;
using (var tin = tinLayer.GetTinDataset())
{
  using (var tinDef = tin.GetDefinition())
  {
    extent = tinDef.GetExtent();
    sr = tinDef.GetSpatialReference();
  }
}

using (var terrain = terrainLayer.GetTerrain())
{
  using (var terrainDef = terrain.GetDefinition())
  {
    extent = terrainDef.GetExtent();
    sr = terrainDef.GetSpatialReference();
  }
}

using (var lasDataset = lasDatasetLayer.GetLasDataset())
{
  using (var lasDatasetDef = lasDataset.GetDefinition())
  {
    extent = lasDatasetDef.GetExtent();
    sr = lasDatasetDef.GetSpatialReference();
  }
}