Geodesic
Naturally reductive homogeneous $(\alpha ,\beta )$-metric spaces
Archivum mathematicum, Tome 57 (2021) no. 1, pp. 1-11
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In the present paper we study naturally reductive homogeneous $(\alpha ,\beta )$-metric spaces. We show that for homogeneous $(\alpha ,\beta )$-metric spaces, under a mild condition, the two definitions of naturally reductive homogeneous Finsler space, given in the literature, are equivalent. Then, we compute the flag curvature of naturally reductive homogeneous $(\alpha ,\beta )$-metric spaces.
In the present paper we study naturally reductive homogeneous $(\alpha ,\beta )$-metric spaces. We show that for homogeneous $(\alpha ,\beta )$-metric spaces, under a mild condition, the two definitions of naturally reductive homogeneous Finsler space, given in the literature, are equivalent. Then, we compute the flag curvature of naturally reductive homogeneous $(\alpha ,\beta )$-metric spaces.
DOI : 10.5817/AM2021-1-1
Classification : 53C30, 53C60
Keywords: naturally reductive homogeneous space; invariant Riemannian metric; invariant $(\alpha, \beta )$-metric 
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Parhizkar, M.; Salimi Moghaddam, H.R. Naturally reductive homogeneous $(\alpha ,\beta )$-metric spaces. Archivum mathematicum, Tome 57 (2021) no. 1, pp. 1-11. doi: 10.5817/AM2021-1-1

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