No. Product Management is one part within the four areas of marketing a newly developed or altered product to the market that demands it, i.e., Product Development. Product Management is primarily responsible and geared towards defining the products in question, regarding the market. Pricing, promotion and distribution are the other three parts that play heavily into the success of a product.
As such, Product Management deals with questions like, what would the life cycle of the product be, what products should even be produced and sold, what logo would be best for the product, how many of the products to produce at a time and what pre-existing products might a new one make obsolete.