Locally dually flatness and locally projectively flatness of Matsumoto change with m-th root Finsler metrics

Document Type : Original Article


Department of Mathematics and Stataistics, Faculty of Science, Dr. Rammanohar Lohia Avadh University, Ayodhya-224001, India. E-mail: mvermamath@gmail.com and mkvermabhu1986@gmail.com


In this paper, we study the Matsumoto change of m-th root Finsler metric. We find the necessary and sufficient conditions under which the transformed metric be locally dually flat. Also, we prove that for Matsumoto change of m-th root metric is locally projectively flat if and only if it is locally Minkowskian.