public DatabaseConnectionFile( 
   Uri path
)

public async Task OpenEnterpriseGeodatabaseUsingSDEFilePath()
{
  await ArcGIS.Desktop.Framework.Threading.Tasks.QueuedTask.Run(() =>
  {
    using (Geodatabase geodatabase = new Geodatabase(new DatabaseConnectionFile(new Uri("path\\to\\sde\\file\\sdefile.sde"))))
    {
      // Use the geodatabase.
    }
  });
}

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");
    }
  });
}