Naturally reductive homogeneous ( α , β ) -metric spaces

M. Parhizkar; H.R. Salimi Moghaddam

Archivum Mathematicum (2021)

  • Volume: 057, Issue: 1, page 1-11
  • ISSN: 0044-8753

Abstract

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In the present paper we study naturally reductive homogeneous ( α , β ) -metric spaces. We show that for homogeneous ( α , β ) -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 ( α , β ) -metric spaces.

How to cite

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Parhizkar, M., and Salimi Moghaddam, H.R.. "Naturally reductive homogeneous $(\alpha ,\beta )$-metric spaces." Archivum Mathematicum 057.1 (2021): 1-11. <http://eudml.org/doc/297246>.

@article{Parhizkar2021,
abstract = {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.},
author = {Parhizkar, M., Salimi Moghaddam, H.R.},
journal = {Archivum Mathematicum},
keywords = {naturally reductive homogeneous space; invariant Riemannian metric; invariant $(\alpha ,\beta )$-metric},
language = {eng},
number = {1},
pages = {1-11},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Naturally reductive homogeneous $(\alpha ,\beta )$-metric spaces},
url = {http://eudml.org/doc/297246},
volume = {057},
year = {2021},
}

TY - JOUR
AU - Parhizkar, M.
AU - Salimi Moghaddam, H.R.
TI - Naturally reductive homogeneous $(\alpha ,\beta )$-metric spaces
JO - Archivum Mathematicum
PY - 2021
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 057
IS - 1
SP - 1
EP - 11
AB - 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.
LA - eng
KW - naturally reductive homogeneous space; invariant Riemannian metric; invariant $(\alpha ,\beta )$-metric
UR - http://eudml.org/doc/297246
ER -

References

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  12. Matsumoto, M., The Berwald connection of a Finsler space with an ( α , β ) -metric, Tensor, N.S. 50 (1991), 18–21. (1991) MR1156480
  13. Matsumoto, M., 10.1016/0034-4877(92)90005-L, Rep. Math. Phys. 31 (1992), 43–83. (1992) MR1208489DOI10.1016/0034-4877(92)90005-L
  14. Moghaddam, H.R. Salimi, 10.1088/1751-8113/41/27/275206, J. Phys. A: Math. Theor. 41 (2008), 6 pp., 275206. (2008) MR2455543DOI10.1088/1751-8113/41/27/275206
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  16. Shen, Z., Lectures on Finsler Geometry, World Scientific, 2001. (2001) Zbl0974.53002MR1845637

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