The WebHDFS APIs, provided as part of Hadoop, are available. The full description of API calls is available in the WebHDFS documentation.
LucidWorks Big Data proxies the WebHDFS APIs, meaning that to access it, you must refer to the Big Data hostname and port, and preface calls with sda/v1/webhdfs.
For example, a valid WebHDFS call to list the "/" directory would be:
curl http://localhost:50070/webhdfs/v1?op=LISTSTATUS
To do the same call with the Big Data system, you would replace the http://localhost:50070/webhdfs/v1 section of the call with http://localhost:8341/sda/v1/webhdfs, as so:
curl -u administrator:foo http://localhost:8341/sda/v1/webhdfs/?op=LISTSTATUS