Mikhail Baryshnikov was stunned when he first set eyes on Julie Cox two years ago. Just 16 at the time, she had joined an audition for the American Ballet Theatre in New York with little expectation of being picked out of the crowd. But Baryshnikov immediately envisioned a future romantic role for the lithe young ballerina. "I was absolutely mesmerized by her looks," Baryshnikov says. "She has really an extraordinary face, a classic face."

Haunted by that face, Baryshnikov recommended that Cox co-star with him in the new film Dancers. (At his suggestion, she took the stage name Julie Kent.) He is typecast as a legendary ballet star and lady-killer; she plays a demure young dancer who falls prey to his charms. A novice who landed the part without a screen test, Kent has yet to recover from her shock when Baryshnikov sought her for the movie. "I was like wow, wow, wow, wow!" she says. In the meantime, Kent's prospects for becoming a prima ballerina seem bright. Last summer she was one of a handful of dancers who performed with Baryshnikov on a national tour. Now in her second season in the corps de ballet of ABT, she is already dancing solos in The Sleeping Beauty.

It is all a very heady experience for Kent, until recently an ordinary Bethesda, Md., high school student and a confirmed homebody. "Oh, I went out," she says. "I went a lot with my mother and sister to the ballet." She inherited a love for dance from her mother, Jennifer, a ballet teacher, and her talent earned her first prize at the 1986 Prix de Lausanne international ballet competition in Switzerland. "When she does an arabesque, her body is endless," Kent's former instructor, Tensia Fonseca, says of her 5'5½", 100-lb. protégée. "She looks like she is floating on air."

For the moment, of course, she is. And so far, despite Baryshnikov's reputation, his wooing of her has been purely professional. Kent insists she was much too intimidated by him to feel any romantic attraction. "If I had stopped to think, 'Oh my gosh, I'm in a movie with Mikhail Baryshnikov,' " she giggles, "I would have freaked out."