Abstract
Two Finsler metrics on a manifold are said to be (pointwise) projectively related (projectively equivalent in an alternative terminology in [13]), if they have the same geodesics as point sets.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
X. Cheng, Z. Shen, On Douglas metrics. Publ. Math. Debr. 66, 503–512 (2007)
G. Chen, X. Cheng, A class of Finsler metrics projectively related to a Randers metric. Publ. Math. Debr. 81, 351–363 (2012)
X. Cheng, Z. Shen, Finsler Geometry, An Approach via Randers Space (Science Press, Beijing, 2012)
N. Cui, Y. Shen, Projective change between two classes of(α, β)-metrics. Differ. Geom. Appl. 27, 566–573 (2009)
L. Huang, X. Mo, On spherically symmetric Finsler metrics of scalar curvature. J. Geom. Phys. 62, 2279–2287 (2012)
B. Li, Z. Shen, On Randers metrics of quadratic Riemann curvature. Int. J. Math. 20, 369–376 (2009)
H. Liu, X. Mo, Examples of Finsler metrics with special curvature properties. Math. Nachr. 288, 1527–1537 (2015)
M. Matsumoto, Projective changes of Finsler metrics and projectively flat Finsler spaces. Tensor N. S. 34, 303–315 (1980)
X. Mo, On the non-Riemannian quantity H of a Finsler metric. Differ. Geom. Appl. 27, 7–14 (2009)
X. Mo, Finsler metrics with special Riemannian curvature properties. Differ. Geom. Appl. 48, 61–71 (2016)
X. Mo, N.M. Solorzano, K. Tenenblat, On spherically symmetric Finsler metrics with vanishing Douglas curvature. Differ. Geom. Appl. 31, 746–758 (2013)
B. Najafi, Z. Shen, A. Tayebi, On a projective class of Finsler metrics. Publ. Math. Debr. 70, 211–219 (2007)
Y. Shen, Y. Yu, On projectively related Randers metrics. Int. J. Math. 19, 503–520 (2008)
Z. Shen, On R-quadratic Finsler spaces. Publ. Math. Debr. 58, 263–274 (2001)
Z. Shen, On projectively related Einstein metrics in Riemann-Finsler geometry. Math. Ann. 320, 625–647 (2001)
C. Yu, H. Zhu, On a new class of Finsler metrics. Differ. Geom. Appl. 29, 244–254 (2011)
Y. Yu, Y. You, Projective equivalence between an (α, β)-metric and a Randers metric. Publ. Math. Debr. 82, 155–162 (2013)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd., part of Springer Nature
About this chapter
Cite this chapter
Guo, E., Mo, X. (2018). Spherically Symmetric W-Quadratic Metrics. In: The Geometry of Spherically Symmetric Finsler Manifolds. SpringerBriefs in Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-13-1598-5_8
Download citation
DOI: https://doi.org/10.1007/978-981-13-1598-5_8
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-1597-8
Online ISBN: 978-981-13-1598-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)