I am working as an undergraduate research assistant for a professor in the mathematics department, on a specific project. Looking at the project I realized that there may be connections to a different area of mathematics that my supervisor doesn't specialize in, that could provide a potentially new research direction. I have previously met another professor who specializes in the connected research area, and he told me to stay in touch. Would it be appropriate for me to tell the other professor about my idea, and ask him if he is aware of any research papers on the topic? He is quite busy as it is so I don't think he would be interested in joining in on the project, I more just wanted his advice about whether this idea makes sense and if there is any previous research about it. A google search did not reveal any related papers, but I am wondering if there may be some papers out there with a more niche title that I wouldn't think to search.
Would this be appropriate? I am very new to researching and academia so I am not too sure about the politics of it all and would greatly appreciate some advice.