The body of Olivet, 43, was discovered in his apartment in the 2800 block of Fleming Drive, off Lumpkin Road, around 2 p.m.
Warrants have been filed for Carl Garland Logan for murder and possession of a knife during the commission of a crime, sheriff’s Sgt. Bill Leisey said.
Police are still investigating the circumstances that led to the death.
“It was not random,” Leisey said. “We do know they were friends.”
Lt. Blaise Dresser said investigators do not believe Logan is still in Augusta, but that he possibly fled to North Carolina or Virginia.
Danville authorities also have warrants for Logan stemming from an earlier stabbing incident there. Police said that victim did not die as a result of the incident.