Abstract
A Finsler space has been shown to satisfy theT-condition if the Finslerian metric tensor is quadratic in the unit tangent vectors. In the case where the curvature tensor of the indicatrix vanishes the converse statement is valid. The wide class of the Finslerian metric functions satisfying the condition of the quadratic dependence of the metric tensor on the unit tangent vectors, and hence theT-condition, has been found.
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References
Asanov, G. S.,New examples of S3-like Finsler spaces. Rep. Math. Phys.16 (1979), 329–333.
Rund, H.,The differential geometry of Finsler spaces. Springer, Berlin, 1959. (Russian translation: Nauka, Moscow, 1981.)
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Asanov, G.S., Kirnasov, E.G. On finsler spaces satisfying theT-condition. Aeq. Math. 24, 66–73 (1982). https://doi.org/10.1007/BF02193035
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DOI: https://doi.org/10.1007/BF02193035