In this note, some basic structural conditions that are imposed on a Finsler manifold as a consequence of existence of a conformal gradient field are presented. Then, after reiterating the definition of warped product Finsler manifolds and the constituents of its related variational problem, the correlation between geodesics of this warped product structure and geodesics of its constructing Finsler manifolds is studied.
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H. Akbar-Zadeh, Transformations infinitésimales conformes des variétés finsleriennes compactes. Ann. Polon. Math. XXXVI, 213–229 (1979)
G.S. Asanov, Finslerian metric functions over the product \(R \times M\) and their potential applications. Rep. Math. Phys. 41, 117–132 (1998)
D. Bao, S.S. Chern, Z. Shen, Riemann–Finsler geometry (Springer, Berlin, 2000)
B. Bidabad, P. Joharinad, Conformal vector fields on complete Finsler spaces of constant Ricci curvature. J. Differ. Geom. Appl. 33, 75–84 (2014)
H.W. Brinkmann, Einstein spaces which are mapped conformally on each other. Math. Ann. 94, 119–145 (1925)
P. Joharinad, Warped product Finsler manifolds from Hamiltonian point of view. Int. J. Geom. Methods Mod. Phys. 14(2), 1750029-1–1750029-16 (2017)
P. Joharinad, B. Bidabad, Conformal vector fields on Finsler spaces. J. Differ. Geom. Appl. 31, 33–40 (2013)
L. Kozma, I.R. Peter, V. Varga, Warped product of Finsler manifolds. Ann. Univ. Sci. Bp. Eotvos Sect. Math. 44, 157–170 (2001)
Z. Shen, Lectures on Finsler Geometry (World Scientific Pub Co Inc, Singapore, 2001)
Z. Shen, Differential Geometry of Spray and Finsler Spaces (Kluwer, Dordrecht, 2001)
Y. Tashiro, Complete Riemannian manifolds and some vector fields. Trans. AMS 117, 251–275 (1965)
K. Yano, The Theory of Lie Derivatives and Its Applications (North Holland, Amsterdam, 1957)
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Joharinad, P. Conformal gradient fields on Finsler manifolds. Period Math Hung 82, 87–97 (2021). https://doi.org/10.1007/s10998-020-00330-5
- Finsler manifolds
- Conformal gradient fields
- Warped product
Mathematics Subject Classification