The project manager is not a prescribed role in the Agile framework. Project managers are traditionally responsible for balancing scope, schedule, cost/resources, and quality and reporting on risk and progress. Agile "project management" divides some of these responsibilities among the three primary Agile roles:
The Product Manager sets (and continuously reprioritizes) the scope, makes tradeoffs between scope and schedule, and manages stakeholder expectations about these. The time box (schedule) is fixed to the consistent length of a sprint and/or program increment, and the resources are fixed (in terms of stable teams).
The Product Owner sets (and continuously reprioritizes) the scope, makes tradeoffs between scope and schedule, and manages stakeholder expectations about these. The time box (schedule) is fixed to the consistent length of a sprint and/or program increment, and the resources are fixed (in terms of stable teams).
The Agile team directly handles the task assignment, progress reporting, and quality control.
The Scrum Master facilitates the process, removes or escalates impediments, drives the team to inspect and adapt for performance improvement, and makes the progress visible.
In a transformed Agile enterprise, change is recognized as constant and would be funded at a value stream level rather than a project level. However, in an enterprise where some change is funded and tracked outside the primary development stream, project managers are needed to manage "up" so that Agile teams can be successful within the framework.
When an Agile methodology is applied to a project, it is the responsibility of the project manager to ...
Track, manage, and report on project cost and risks.
Track Agile Metrics and report on Metric Trends
Like a Scrum Master, and Agile project manager is a servant leader. Project management is a cooperative effort in Agile; and within the team, titles are left at the door as everyone is accountable for success.
Blog [free]: "The Role of the Project Manager in Agile Development" by Ulf Eriksson (April, 2015)