On generalized Douglas-Weyl Randers metrics

Tayebeh Tabatabaeifar; Behzad Najafi; Mehdi Rafie-Rad

Czechoslovak Mathematical Journal (2021)

  • Issue: 1, page 155-172
  • ISSN: 0011-4642

Abstract

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We characterize generalized Douglas-Weyl Randers metrics in terms of their Zermelo navigation data. Then, we study the Randers metrics induced by some important classes of almost contact metrics. Furthermore, we construct a family of generalized Douglas-Weyl Randers metrics which are not R -quadratic. We show that the Randers metric induced by a Kenmotsu manifold is a Douglas metric which is not of isotropic S -curvature. We show that the Randers metric induced by a Kenmotsu or Sasakian manifold is not Einsteinian. By using D -homothetic deformation of a Kenmotsu or Sasakian manifold, we construct a family of generalized Douglas-Weyl Randers metrics and show that the Lie group of projective transformations does not act transitively on the set of generalized Douglas-Weyl Randers metrics.

How to cite

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Tabatabaeifar, Tayebeh, Najafi, Behzad, and Rafie-Rad, Mehdi. "On generalized Douglas-Weyl Randers metrics." Czechoslovak Mathematical Journal (2021): 155-172. <http://eudml.org/doc/296950>.

@article{Tabatabaeifar2021,
abstract = {We characterize generalized Douglas-Weyl Randers metrics in terms of their Zermelo navigation data. Then, we study the Randers metrics induced by some important classes of almost contact metrics. Furthermore, we construct a family of generalized Douglas-Weyl Randers metrics which are not $R$-quadratic. We show that the Randers metric induced by a Kenmotsu manifold is a Douglas metric which is not of isotropic $S$-curvature. We show that the Randers metric induced by a Kenmotsu or Sasakian manifold is not Einsteinian. By using $D$-homothetic deformation of a Kenmotsu or Sasakian manifold, we construct a family of generalized Douglas-Weyl Randers metrics and show that the Lie group of projective transformations does not act transitively on the set of generalized Douglas-Weyl Randers metrics.},
author = {Tabatabaeifar, Tayebeh, Najafi, Behzad, Rafie-Rad, Mehdi},
journal = {Czechoslovak Mathematical Journal},
keywords = {generalized Douglas-Weyl metric; Randers metric; Kenmotsu manifold; Sasakian manifold},
language = {eng},
number = {1},
pages = {155-172},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On generalized Douglas-Weyl Randers metrics},
url = {http://eudml.org/doc/296950},
year = {2021},
}

TY - JOUR
AU - Tabatabaeifar, Tayebeh
AU - Najafi, Behzad
AU - Rafie-Rad, Mehdi
TI - On generalized Douglas-Weyl Randers metrics
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 155
EP - 172
AB - We characterize generalized Douglas-Weyl Randers metrics in terms of their Zermelo navigation data. Then, we study the Randers metrics induced by some important classes of almost contact metrics. Furthermore, we construct a family of generalized Douglas-Weyl Randers metrics which are not $R$-quadratic. We show that the Randers metric induced by a Kenmotsu manifold is a Douglas metric which is not of isotropic $S$-curvature. We show that the Randers metric induced by a Kenmotsu or Sasakian manifold is not Einsteinian. By using $D$-homothetic deformation of a Kenmotsu or Sasakian manifold, we construct a family of generalized Douglas-Weyl Randers metrics and show that the Lie group of projective transformations does not act transitively on the set of generalized Douglas-Weyl Randers metrics.
LA - eng
KW - generalized Douglas-Weyl metric; Randers metric; Kenmotsu manifold; Sasakian manifold
UR - http://eudml.org/doc/296950
ER -

References

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