Could this be The Chronicles of Riddick ?
There's a scene where various characters are climbing an outcrop.
When the sun touches them, they burn horribly.
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This could be The Mole People , best known for its appearance during the eighth season of Mystery Science Theater 3000 .
A group of mountaineering explorers (led by Shirley Temple's ex-husband, the extremely "moist" John Agar) discover an underground remnant of the ancient Sumerian civilization, where the people are so lacking in melanin that sunlight instantly sunburns them to death.
This is used as a form of ritual execution for criminals, and protagonists use the sunlight to protect them during their escape.
There is also a lot of climbing (prompting the riff:
"This movie is nothing but ropes and asses!").
The plot summary, per Wikipedia : A narration by Dr. Frank Baxter, an English professor at the University of Southern California, explains the premise of the movie and its basis in reality.
He briefly discusses the hollow earth theories of John Symmes and Cyrus Teed among others, and says that the movie is a fictionalized representation of these unorthodox theories.
Archaeologists Dr. Roger Bentley and Dr. Jud Bellamin find a race of Sumerian albinos living deep under the Earth.
They keep mutant humanoid mole men as their slaves to harvest mushrooms, which serve as their primary food source.
The Sumerian albinos' ancestors relocated into the subterranean after cataclysmic floods in ancient Mesopotamia.
They believe the men are messengers of Ishtar, their goddess.
Whenever their population increases, they sacrifice old people to the Eye of Ishtar.
These people have lived underground for so long that they are weakened by bright light which the archaeologists brought in the form of a flashlight.
However, there is one girl named Adad who has natural Caucasian skin who is disdained by the others since she has the "mark of darkness."
When one of the archaeologists is killed by a mole person, Elinu, the High Priest, realizes they are not gods.
He orders their capture and takes the flashlight to control the Mole People, not knowing it is depleted.
The archaeologists are then sent to the Eye of Ishtar just as the Mole People rebel.
Adad goes to the Eye only to realize it is really natural light coming from the surface and that the men had survived.
They then climb to the surface.
Unfortunately, Adad dies after reaching the surface when an earthquake causes a column to fall over and crush her.
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Could this be Missile to the Moon as per Movie about the sun being too hot it burned and kill very fast ? ....
Right near the end the lunar astronauts are trying to evade "rock men" while staying in the shadows.
One astronaut, escaped convict stowaway Gary, refuses to drop the bags of diamonds he has collected.
With the extra weight he is not quick enough to manage.
The film has men climbing up a rock face, and having to stay in the shadows, or else they will be burned, as seen in the case of Gary.
The full film is on YouTube:
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In addition to other answers this could be any number of vampire films, but it makes me think in particular of 1987's Near Dark, in which the protagonist is a vampire and hiding in shadows / burning in sunlight is a recurring theme.
Trailer:
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This reminded me of the Ray Bradbury story Frost and Fire , which was made into a film, Quest , in 1984.
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Might the answer be the movie "Core", in which the earth loses its protective magnetic field?
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In the movie there are several people running into the shadows to hide from the sun that kills them. Whenever the sun hits them, they start to burn alive. I remember one scene where they are climbing on a mountain away from the sun that burns them.
People running into the shadows to hide from killer sunlight, climbing scene
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<story-identification><movie>
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There are a number of films that could fit this description. One is potentially the Chronicles of Riddick. Other potential films with these story elements include The Mole People, Missile to the Moon or Quest. There are a number of possibilities, including The Chronicles of Riddick, The Mole People, Missile to the Moon, Quest or a vampire movie.
It could be The Chronicles of Riddick where various characters clinbing a mountain are badly burned by the sun. It could be The Mole People, where mountaineering explorers discover people who have been living underground for centuries and have lost all their melanin. It could be Missile to the Moon, a movie in which the sun was too hot and it burned and killed very fast. It could be a number of vampire films, but it makes me think in particular of 1987's Near Dark, in which the protagonist is a vampire and hiding in shadows / burning in sunlight is a recurring theme.  This reminds me of the Ray Bradbury story Frost and Fire, which was made into a film, Quest, in 1984. It could be the movie "Core", in which the earth loses its protective magnetic field?