A 28-year-old MIT graduate student was killed in northern India after apparently falling down a cliff while running on a remote mountain trail nine days ago, the school said Sunday. The body of Kaitlin R. Goldstein was found in a ravine below the trail near Leh on Saturday after a weeklong search, the university said in a statement. Investigators, the school said, believe Goldstein slipped on a loose rock and slid several hundred feet down a cliff on June 14. “As Kate’s family and friends bear this sorrow, we offer them the sympathy and support of the MIT community,” president L. Rafael Reif wrote in an e-mail to students, faculty, and staff at the Massachusetts Institute of Technology. “The death of someone so young and promising is a terrible loss; we should all take time to reach out to those around us.” The school said Goldstein’s parents, who are from Providence, flew to India to help with the investigation. Goldstein, who was studying architecture and building technology, was in the Indian state of Jammu and Kashmir to participate at a weeklong workshop on energy and development organized in part by MIT. Then she planned to stay and help install solar panels at a Buddhist monastery, the school said.