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China’s churlish reaction to Barack Obama’s visit to New Delhi this week suggests that the US president and Narendra Modi, the Indian prime minister, are on to something important in their attempt to remake the geostrategic map of the world.

One official Chinese commentary called Mr Obama’s three-day trip — the first time a US president has visited India twice while in office — and his newfound friendship with Mr Modi a “superficial rapprochement . . . given their hard differences on issues like climate change, agricultural disputes and nuclear energy co-operation”.

That prompted one senior US official to say drily it was “notable” that Beijing should go out of its way to comment on the Obama trip. Another officially sanctioned article in Beijing, meanwhile, accused the west of plotting craftily to lure India into a needless confrontation with China.

For all the anticipation among business leaders about multibillion-dollar Indian infrastructure projects, the fast-tracking of US investments in civil nuclear power and a future quintupling of bilateral trade (now $100bn a year), Mr Obama’s trip was really about forging an India-US alliance in the Asia-Pacific region.

Indian politicians and US chief executives know it will be many years before a Westinghouse-made nuclear power plant actually starts feeding electricity to the Indian grid, if it happens at all.

But both sides had invested so much political capital in the long-stalled civil nuclear deal, which involved freeing India’s nuclear electric industry from international sanctions, that this week’s announcement of a breakthrough in the legal negotiations over fuel supplies and accident liability was “a kind of catharsis”, according to Milan Vaishnav of the Carnegie Endowment for International Peace, a think-tank.

Soothing away such irritants allowed Mr Obama and Mr Modi to get on with their core business. It was no coincidence that the agreements finalised during the trip, rather than simply discussed in vaguely optimistic terms for the future, were largely in the fields of defence and diplomacy.

Mr Obama watched Russian-made tanks and fighter planes at India’s Republic Day parade on Monday, but he also had a glimpse of the newly delivered US military transport aircraft that helped make India the biggest foreign buyer of US weapons in 2013 (and allowed the US to overtake Russia as the biggest supplier to India in the same year).

India, now the world’s biggest arms importer, has raised the foreign direct investment limit for arms manufacturing from 26 per cent to 49 per cent, and is eager to have US and other foreign companies transfer technology to India.

“India is on the verge of creating a military-industrial complex of its own,” Anand Mahindra, who heads the Mahindra Group conglomerate, said admiringly before meeting Mr Obama this week.

All this is a commercial worry for Russia. But for China, the most galling aspect of the Obama visit was an unexpected document entitled “US-India Joint Strategic Vision for the Asia-Pacific and the Indian Ocean Region”.

One sentence — a clear message to Beijing about a hotly disputed area of the Pacific far from Indian shores and claimed almost in its entirety by China — demanded freedom of navigation and overflight “especially in the South China Sea”.

Mr Obama and Mr Modi, the latter still smarting from an incursion by hundreds of Chinese troops across the disputed India-China Himalayan border to coincide with President Xi Jinping’s India visit last year, tacitly contrasted Chinese authoritarianism with their own declared respect for freedom, democracy and the rule of law.

Mr Modi is not saddled with the historical baggage of anti-capitalism and suspicion of the west that made the Congress party lean towards the Soviet Union while publicly adopting “non-alignment” during the cold war. Instead, he finds himself propelled into a friendship with Mr Obama by 3m Indian-Americans, many of them prosperous entrepreneurs hailing from his native Gujarat.

“Modi comes in and finds that there is much greater strategic convergence with the US vis-à-vis China,” says Mr Vaishnav. “He doesn’t have this historical ideological baggage” and is not embarrassed about openly befriending the US. “That,” Mr Vaishnav says, “has to be counted as a significant break from the past.”