Final answer:
Incident escalation to an incident manager due to the failure of a solution team to resolve an issue within the required time typically refers to hierarchical escalation within the IT service management framework.
Step-by-step explanation:
When a serious incident occurs and the solution team assigned to the incident is unable to resolve it within the agreed-upon time frame, and as a result, the incident is escalated to the incident manager, this is known as incident escalation. In a business context, specifically within IT service management and ITIL frameworks, there are two types of escalations: functional escalation and hierarchical escalation. Given the scenario where the incident manager becomes involved, we are likely dealing with hierarchical escalation, which occurs when the resolution of the incident necessitates a higher level of authority or additional resources beyond the current capability.