On evolution of Finsler Ricci scalar
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Here, we calculate the evolution equation of the reduced $hh$-curvature and the Ricci scalar along the Finslerian Ricci flow. We prove that Finsler Ricci flow preserves positivity of the reduced $hh$-curvature on finite time. Next, it is shown that evolution of Ricci scalar is a parabolic-type equation and moreover if the initial Finsler metric is of positive flag curvature, then the flag curvature, as well as the Ricci scalar, remain positive as long as the solution exists. Finally, we present a lower bound for Ricci scalar along Ricci flow.
Abstract
Here, we calculate the evolution equation of the reduced $hh$-curvature and the Ricci scalar along the Finslerian Ricci flow. We prove that Finsler Ricci flow preserves positivity of the reduced $hh$-curvature on finite time. Next, it is shown that evolution of Ricci scalar is a parabolic-type equation and moreover if the initial Finsler metric is of positive flag curvature, then the flag curvature, as well as the Ricci scalar, remain positive as long as the solution exists. Finally, we present a lower bound for Ricci scalar along Ricci flow.
참고문헌 (15)
- H. Akbar-Zadeh, "Initiation to Global Finslerian Geometry, North-Holland Mathematical Library, 68" (2006), Elsevier Science B.V.
- S. Azami, "Existence and uniqueness for solution of Ricci flow on Finsler manifolds", Int. J. Geom. Methods Mod. Phys., 10(3), pp.21~ (2013)
- D. Bao, "Finsler geometry, Sapporo 2005-in memory of Makoto Matsumoto", pp.19~71 (2007), Math. Soc. Japan
- D. Bao, "An Introduction to Riemann-Finsler Geometry, Graduate Texts in Mathematics, 200" (2000), Springer-Verlag
- D. Bao, "On the volume of unit tangent spheres in a Finsler manifold", Results Math., 26(1-2), pp.1~17 (1994)[DOI]
- B. Bidabad, "Hamilton's Ricci Flow on Finsler Spaces", arXiv:1508.02893, ~ (2015)
- B. Bidabad, "Ricci flow on Finsler surfaces", J. Geom. Phys. (2018)
- Behroz Bidabad, "Deformation of Cartan curvature on Finsler manifolds", 대한수학회보, 54(6), pp.2119~2139 (2017), 대한수학회
- B. Bidabad, "On quasi-Einstein Finsler spaces", Bull. Iranian Math. Soc., 40(4), pp.921~930 (2014)
- S. Lakzian, "Differential Harnack estimates for positive solutions to heat equation under Finsler-Ricci flow", Pacific J. Math., 278(2), pp.447~462 (2015)[DOI]
- B. Shen, "Twisted Ricci flow on a class of Finsler metrics and its solitons", Differential Geom. Appl., 46, pp.132~145 (2016)[DOI]
- P. Topping, "Lectures on the Ricci Flow, London Mathematical Society Lecture Note Series, 325" (2006), Cambridge University Press
- S. I. Vacaru, "Metric compatible or non-compatible Finsler-Ricci flows", Int. J. Geom. Methods Mod. Phys., 9(5), pp.26~ (2012)
- M. Yarahmadi, "On compact Ricci solitons in Finsler geometry", C. R. Math. Acad. Sci. Paris, 353(11), pp.1023~1027 (2015)[DOI]
- M. Yarahmadi, "Convergence of Finslerian metrics under Ricci flow", Sci. China Math., 59(4), pp.741~750 (2016)[DOI]