Ricci_Curvature_of_Finsler_Metrics_by_Warped_Product.pdf (529.58 kB)

Ricci Curvature of Finsler Metrics by Warped Product

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posted on 01.05.2020, 18:14 by Patricia Marcal
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.

Funding

CNPq-Brazil, 217974/2014-7

History

Degree Type

Doctor of Philosophy

Department

Mathematics

Campus location

Indianapolis

Advisor/Supervisor/Committee Chair

Zhongmin Shen

Additional Committee Member 2

Olguta Buse

Additional Committee Member 3

Daniel Ramras

Additional Committee Member 4

Roland Roeder

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