In President Trump’s newly published “Save America,” a coffee-table picture book, he writes that the first of his three meetings with Kim Jong-un had shown that “real change is indeed possible” and that they had gotten “to know each other well in a confined period of time.”

It was at the summit between Trump and Kim at Singapore in June 2018 that they struck up a relationship that showed “real change is possible,” he wrote, raising hopes for “a glorious new era of security and prosperity for his people” after decades of hostility dating to the Korean War.

South Korean diplomats tell the Sun that Trump’s commentary, on top of his remarks about his bond with Mr. Kim, is raising concerns that should he return to the White House, the durability of Seoul’s historic alliance with Washington would be in doubt.

It’s not just Trump’s claims to have fallen “in love” with Mr. Kim but rather his insistence, as repeated in the book, that South Korea should “start paying more money for defense.” That’s a reminder that, as president, he had wanted the South to pay five times the current level of about a billion dollars a year for American troops and bases in Korea.

A former ambassador to Korea during Trump’s presidency, Harry Harris, sees a dour outlook among South Koreans whom he came to know well. A retired admiral who once commanded American forces in the Pacific, Mr. Harris was critical of Trump’s decision, immediately after the Singapore summit, to cancel war games involving American and South Korean troops.

“Our military readiness actually decreased because of the prohibition against military exercises,” Seoul’s Yonhap News quotes him as saying in a video link with the Korea Development Institute in Seoul and Johns Hopkins’ School of Advanced International Studies in Washington. It was “naive to think,” he said, that Mr. Kim would “ever give up his nuclear weapons.”

While Trump often refers to the relationship that he formed with Mr. Kim in Singapore, he prefers not to dwell on the failure of their second summit in Hanoi in February 2019.

A photograph in his new book shows the 45th president and Mr. Kim in the lobby of the Hotel Metropole in Hanoi. That was before Trump walked out of the meeting, skipping a lavish lunch for the American and North Korean teams, after Mr. Kim balked at giving up his nuclear weapons program despite agreeing to close the main nuclear facility at Yongbyon, north of Pyongyang.

Nor does the book dwell on Trump’s third and final meeting with Mr. Kim, at the truce village of Panmunjom on the North-South line 40 miles north of Seoul in June 2019. That was what Mr. Harris called “the snap summit” — a chat agreed on after Trump had met the then-president of South Korea, Moon Jae-in, in Seoul. Trump suggested working-level talks with the North Koreans, which never happened.

The book features pictures of Trump and Mr. Kim on the North-South line, and of Trump and Mr. Moon and their wives, Melania and Kim Jung-sook. That was nearly three years before a conservative, Yoon Seok-yul, was elected as Mr. Moon’s successor and Mr. Kim declared South Korea “the enemy” with whom he has refused all contact.