During the convalescence of the Pope John Paul II the day-to-day affairs of the Roman Catholic Church will be handled by the Vatican's administrative arm, the Roman Curia, just as it would operate if the pope were on a tour abroad.

The Vatican Secretariat of State, which handles both internal and external affairs, routinely coordinates all curial operations and is geared to keep the church functioning whether the pope is in the Vatican or not.

Ironically, Cardinal Agostino Casaroli, the secretary of state, was en route to the United States to receive an honorary degree at St. John's University on Long Island when the pope was shot. He was to board a return flight to Rome as soon as he arrived at New York's Kennedy Airport yesterday afternoon.

In addition to the Vatican Secretary of State, John Paul's own personal staff is accustomed to handling church affairs during his absence. Because of the pontiff's many trips since taking office nearly three years ago, the Vatican today is probably better prepared to function for a few weeks without the pope's direct hand than at any time in recent history.

There are, however, a number of functions which, by church law or by his own ruling, only the pope can perform. Although it is not known how long the pontiff will be incapacitated, the attack on his life may affect the church in a number of areas.

The insurance of a long-awaited revised code of canon law, in preparation for more than a decade, had been expected early this summer and, unless he has already approved the document, may be delayed by his convalescence.

His injuries will probably force cancellation of a trip next month to Switzerland and the World Council of Churches headquarters in Geneva, especially important because of widespread grumbling among Protestants that the Polish-born pontiff has been dragging his feet on church unity.

Appointments to major church posts throughout the world also require papal approval. There has been considerable speculation that Pope John Paul would call a consistory this spring to name new members to the College of Cardinals, possibily including some American churchmen.

Another function which Pope John Paul has reserved for himself, although he is not obliged by church law to do so, is the processing of the thousands of applications from priests who seek to leave the priesthood and to be excused from their vows of celibacy.

Two decades ago, Pope Pius XII was virtually incapacitated by illness for the last year or two of his pontificate until his death in 1958, but the Vatican continued to function under the leadership of the secretary of state.

Although John Paul II is the first pontiff to have suffered gunshot wounds, a number of popes throughout history, but mostly in the early days of the church, have been the victims of attacks, assassinations or some other violent death.

In 1970, Pope Paul VI received a knife wound when he was attacked during a visit to Manila. Even though the wound was considerably more serious than was revealed at the time, the pope kept to his schedule "to avoid setting off mass hysteria," Bishop Thomas C. Kelly, head of the National Conference of Catholic Bishops, said yesterday.

According to the Rev. Robert Trisco of Catholic University, "the last Pope to die a violent death was Pope John XIV" in 984. Caught in a political struggle between the German-born Emperor Otto II and the Romans. John was captured by the Romans after Otto's death "and died of assassination or starvation, we don't know which," said Trisco.

The death of Pius VI in 1799 was accelerated when, as an already sick man, he was carried off by the French under Napoleon Bonaparte and died a prisoner in Valence, France.

St. Peter, the first pope, was crucified in Rome around 67 A.D., and his 14 immediate successors are also believed to have been martyred.

In all, according to the Association Press, more than 30 popes died violent deaths nearly half of that number of poisoning or by the sword. But since the Renaissance, most people have died in their beds of natural causes.

Unlike the provisions for the passage of power in the death of a president of this country, the death of a pope brings the Vatican to a standstill until a successor is named by the college of cardinals. After the Vatican's secretary of state verifies that a pontiff is dead, his papal ring and seal, the symbols of his office are smashed, all employes of the holy city are considered to have tendered their resignation and "only a holding operation" is in effect, said the Rev. Donald Campion, who was formerly the Jesuit spokesman at the Vatican.

"These elaborate rules have developed to prevent one faction or another from taking over in the transition period," said. Business resumes only when the newly elected pope takes over.