Amirkabir University of Technology AUT Journal of Mathematics and Computing 2783-2449 2 2 2021 09 01 On Finsler warped product metrics with vanishing $E$-curvature 137 142 4408 10.22060/ajmc.2021.19817.1052 EN Ranadip Gangopadhyay DST-CIMS, Banaras Hindu University, Varanasi-221005, India Anjali Shriwastawa DST-CIMS, Banaras Hindu University, Varanasi-221005, India Bankteshwar Tiwari DST-CIMS, Banaras Hindu University, Varanasi-221005, India 0000-0003-4529-8261 Journal Article 2021 04 05 In this paper, we study Finsler warped product metric recently introduced by P. Marcal and Z. Shen and find characteristics differential equations for this metric to have vanishing $E$-curvature. We also prove that if this warped product Finsler metric is projectively flat, then it becomes a Riemannian metric. Finsler metrics Warped product $E$-curvature Projectively flat https://ajmc.aut.ac.ir/article_4408_c793b3be8f18731f2a4c627fb3c6c63d.pdf