You should keep eye contact during a conversation. You're showing her that you're paying complete attention only to her, and nothing else.
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I am talking about making the first connection. Imagine you are in an elevator with a bunch of people. there is this cute girl across from you. how do you make the first connection? isn't the standard advice given here to lock eyes and never break eye contact? or did i misunderstand?
Both of you won't keep eye contact. Eye contact entails looking into her eyes, not at her eyes. It requires for her to be looking back at you, or in some way interacting with you. If she is standing there minding her own business, you should mind your own business OR talk to her if you want to. Once you're talking, then keep eye contact.
If she randomly looks at you before you're talking, look at her and give her a smile. See how she reacts and spark up a conversation.
You should be conveying confidence through eye contact in interactions. If you're not interacting, other social cues should be conveying that confidence instead. (posture, how you're dressed, smiling, etc.)
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