Abstract
In this chapter, we analyze the weighted Ricci curvature for some examples appearing in Chap. 6. We remark that a suitable choice of a measure is unclear in some cases. In fact, the theory of weighted Ricci curvature has so far been focused on general theory and there are not many investigations on concrete examples.
One of the most important observations in this chapter is the absence of “canonical measures” in some Randers spaces. Precisely, we will see that some Randers spaces do not admit any measure whose S-curvature vanishes identically.
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References
Ohta, S.: Vanishing S-curvature of Randers spaces. Differ. Geom. Appl. 29, 174–178 (2011)
Ohta, S.: Weighted Ricci curvature estimates for Hilbert and Funk geometries. Pacif. J. Math. 265, 185–197 (2013)
Shen, Z.: Lectures on Finsler Geometry. World Scientific Publishing Co., Singapore (2001)
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Ohta, Si. (2021). Examples of Measured Finsler Manifolds. In: Comparison Finsler Geometry. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-80650-7_10
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DOI: https://doi.org/10.1007/978-3-030-80650-7_10
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