Because you’re using present continuous in your sentence. I am writing. I am submitting.

"Submitting" is a gerund - a verb acting like a noun. Like swimming, shopping, cycling. You are asking for their participation in an activity. Verbs and nouns have patterns after them and this is how it work with the noun "participation in" and the verb "to participate". A different pattern after the verb help: "Please help me to submit...".