Well, no.
However, there are two different types of handsome gangs out here: the introverted crowd and the extrovert side.
If you're a handsome man with a quiet, introverted demeanor, yes, you may get approached less by women, not because you're ugly, obviously, but because you come across as quiet, shy, etc which might not be her thing due to her personality being more on the extrovert side.
The extroverted, handsome guy will get approached more because he's verbally outgoing and inviting due to his communicative, lively personality; in other words, he brings women closer to him just by being more social.
Sometimes, a quiet, handsome dude will get approached, but that's usually from a woman who is also somewhat introverted herself, so she can relate to his personality, but a very extroverted woman would be the opposite.
As a handsome man, personally, I consider myself to be in the middle, a guy who's quiet at first; during the beginning stages of meeting and vibing with a woman, I might be a bit introverted, some women have told me it felt like I was trying “read” or get a feel of them, shyt my girl now once said when we first started conversing she thought I was like a ninja because of my initial closed book attitude, had her thinking I was hiding something.
Usually, over the course of a week or two, once I've really gotten comfortable with a girl, I'm more extroverted in our discussions and face-to-face interactions

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