University of Mohaghegh Ardabili Journal of Finsler Geometry and its Applications 2783-0500 6 2 2025 12 01 Study of some curvatures with Z. Shen's square metric 41 52 3851 10.22098/jfga.2025.17260.1157 EN Sachin Kumar Department of Mathematics and Statistics, Dr. Rammanohar Lohia Avadh University, Ayodhya(U. P.), India Abhishek Singh Department of Mathematics and Statistics, Dr. Rammanohar Lohia Avadh University, Ayodhya(U.P.), India P. K. Dwivedi Department of Mathematics and Statistics, Dr. Rammanohar Lohia Avadh University, Ayodhya(U.P.), India C. K. Mishra Department of Mathematics and Statistics, Dr. Rammanohar Lohia Avadh University, Ayodhya(U.P.), India Uma Shanker Department of Mathematics and Statistics, Dr. Rammanohar Lohia Avadh University, Ayodhya(U.P.), India Journal Article 2025 04 23 In this research paper, we have studied the Z-Shen square metric under the condition that the 1-form β is a Killing form of constant length. We have derived the explicit expressions for the Ricci and Riemann curvatures associated with this metric. Furthermore, we have investigated the special characteristics of projectively flat Z-Shen square metrics that possess isotropic S-curvature https://jfga.uma.ac.ir/article_3851_6097d308756531c96f4b2e2c5c018f36.pdf