President Carter, determined to pursue nothing much more than fishing, reading and rest, escaped to the seclusion of an offshore Georgia island today to begin a 10-day vacation.

The president, his wife Rosalynn, and daughter Amy arrived in Brunswick, Ga., this morning and flew immediately by helicopter to Sapelo Island, about 30 miles north of here along south Georgia coast.

On the island for the next eight days, the Carters will live in splendid isolation, housed in a century-old Mediterranean-style villa amid lush coastal vegetation.

The president plans to end his vacation with a one-day visit April 20 to his hometown of Plains, Ga., and with a visit April 21 to Calhoun to attend the christening of his granddaughter, Sarah Rosemary. He is scheduled to return to Washington April 21.

White House deputy press secretary Rex Granum said Carter brought relatively little work with him and does not plan to leave the island except for fishing trips. The president may be visited by his longtime friend and adviser, Atlanta lawyer Charles H. Kirbo, while here, Granum said.

Carter has vacationed in the past on nearby St. Simon's Island, staying in a mansion owned by Smith Bagley, heir to the R.J. Reynolds tobacco fortune. But Bagley was indicted last month on fraud and stock manipulation charges, disrupting the president's usual vacation routine.

As an alternative, Carter turned to Sapelo Island, which is owned by the state of Georgia and used mainly for wildlife and marine research.

The 18-mile-long island has a colorful history, dating back to its original settlement by Spanish missionaries in the 16th century.

The villa the Carters will stay in was built in the 19th century and restored in the early 1900s by Hudson Motors magnate Howard Coffin. It was later owned by Bagley's grandfather, tobacco kingpin R.J. Reynolds.

The villa, known as "Big House," contains about a dozen bedrooms, a ballroom, an elegant swimming pool and Italian marble statues.

Granum said the president will pay the "going rates" to the state of Georgia to rent the villa, but neither he nor other officials could say how much that is.

In addition to comfort, the island villa will afford Carter maximum privacy, far from the prying eyes of reporters who are housed miles away on Jekyll Island. White House Officials suggested the president will rarely, if at all, be seen during the next week.

The island is accessible only by boat. Its shoreline is being patrolled by Coast Guard and Georgia state police vessels, and reporters and other outsiders will not be allowed to visit it during the presidential vacation.

Sapelo Island also is the home of 150 families who live in Hog Hammock, a 400-acre settlement that is the only privately owned land on the island. Descendants of slaves, they work for the state marine institute and wildlife preserve that take up most of the island.