Mr. and Mrs. Michael Dombrowsky of West Palm Beach, Fla., announce the engagement of their daughter Miss Christina Nicole Dombrowsky to Mr. Seth Bowen Barnes Jr., son of Mr. and Mrs. Seth Barnes of Gainesville. The bride-elect is the granddaughter of Mr. Alan Dombrowsky and Dr. Susan Dombrowsky of Miami Shores, Fla., and Mr. and Mrs. Bill Matthews of Naples, Fla. She is a 2003 graduate of Cardinal Newman High School in West Palm Beach, Fla.