Why does a man look at you when you’re not looking with an intense, serious expression and even in front of his girlfriend?

He laughs at my jokes, I catch him stealing glances, in the past he has teased me and said and done suggestive things so I know he’s attracted to me. He even stroked my hand with his thumb while looking in my eyes in front of his girlfriend. I told him to keep his distance after that and told him I would be out of respect for his girlfriend. They’ve only dated two months but it seems to be getting serious. They’re visiting each other’s families over the Holiday period. In spite of this we’re in the same friend circle and I catch him stealing glances, and sometimes staring at me with a very intense gaze. The other night I told a joke and he laughed and looked really goofy. His girlfriend was there and she took his arm and started stroking it in quite a possessive and territorial manner I would say. I broadly ignore him these days. I don’t even as much as return the gaze but what is he trying to do here?
Why does a man look at you when you’re not looking with an intense, serious expression and even in front of his girlfriend?
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