Kayhan, HünkarÖzel, Cenap2021-06-232021-06-2320091311-8080https://hdl.handle.net/20.500.12491/4104https://www.scopus.com/inward/record.uri?eid=2-s2.0-78649793883&partnerID=40&md5=7de4af9fd6bfb3be8fda0cdee0004d98We consider the Dirac operator on a six dimensional sphere with gravitational and Yang-Mills gauge fields. Here we calculate the Atiyah-Singer index of Dirac operator on a six dimensional sphere with a 50(6)-gauge theory. Moreover, we take the vector field as to be Hedgehog-connection which gives an appropriate result for the field strength and therefore the topological charge. © 2009 Academic Publications.eninfo:eu-repo/semantics/closedAccessAnomalyAtiyah-Singer IndexDirac OperatorGravitational FieldsHedgehog ConnectionTopological ChargeYang- Mills FieldsArticle5257597662-s2.0-78649793883N/A