10.25394/PGS.12227399.v1 Patricia Marcal Patricia Marcal Ricci Curvature of Finsler Metrics by Warped Product Purdue University Graduate School 2020 Warped Product Finsler Metric Ricci Curvature Ricci flat Algebraic and Differential Geometry Geometry 2020-05-01 18:14:25 Thesis https://hammer.purdue.edu/articles/thesis/Ricci_Curvature_of_Finsler_Metrics_by_Warped_Product/12227399 <div>In the present work, we consider a class of Finsler metrics using the warped product notion introduced by B. Chen, Z. Shen and L. Zhao (2018), with another “warping”, one that is consistent with the form of metrics modeling static spacetimes and simplified by spherical symmetry over spatial coordinates, which emerged from the Schwarzschild metric in isotropic coordinates. We will give the PDE characterization for the proposed metrics to be Ricci-flat and construct explicit examples. Whenever possible, we describe both positive-definite solutions and solutions with Lorentz signature. For the latter, the 4-dimensional metrics may also be studied as Finsler spacetimes.</div>