Amirkabir University of Technology AUT Journal of Mathematics and Computing 2783-2449 3 1 2022 02 01 Locally projectively flatness and locally dually flatness of generalized Kropina conformal change of $m$-th root metric 27 33 4633 10.22060/ajmc.2021.20561.1070 EN Achal Singh Department of Mathematics, Institute of Applied Sciences and Humanities, GLA University Mathura-281406, India Manoj Kumar Department of Mathematics and Statistics, Dr. Rammanohar Lohiya Avadh University, Ayodhya-224001, India Chayan Kumar Mishra Department of Mathematics and Statistics, Dr. Rammanohar Lohiya Avadh University, Ayodhya-224001, India Journal Article 2021 09 14 In this paper, we consider the generalized Kropina conformal change of $m$-th root metric and for this, prove a necessary and sufficient condition of locally projectively flatness. Also we proved a necessary and sufficient condition for the generalized Kropina conformal change of $m$-th root metric is locally dually flat. https://ajmc.aut.ac.ir/article_4633_96c974552b3f2839fcc751e7f12679ce.pdf