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>