Abstract
In this paper, we study the (α, β)-metrics of constant flag curvature. We characterize almost regular (α, β)-metrics of constant flag curvature under the condition that β is a homothetic 1-form with respect to α. Furthermore, we prove that if a regular (α, β)-metric is of constant flag curvature and β is a Killing 1-form with constant length, then it must be a Riemannian metric or locally Minkowskian.
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The second author is supported by the National Natural Science Foundation of China (11871126) and the Science Foundation of Chongqing Normal University (17XLB022).
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Chen, G., Cheng, X. On (α, β)-Metrics of Constant Flag Curvature. Acta Math Sci 42, 755–768 (2022). https://doi.org/10.1007/s10473-022-0220-y
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DOI: https://doi.org/10.1007/s10473-022-0220-y
Key words
- (α, β)-metric
- flag curvature
- S-curvature
- mean Landsberg curvature
- Riemannian metric
- Minkowski metric
- homothetic 1-form