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Here, certain Ricci flow for Finsler $n$-manifolds is considered and deformation of Cartan $hh$-curvature, as well as Ricci tensor and scalar curvature, are derived for spaces of scalar flag curvature. As an application, it is shown that on a family of Finsler manifolds of constant flag curvature, the scalar curvature satisfies the so-called heat-type equation. Hence on a compact Finsler manifold of constant flag curvature of initial non-negative scalar curvature, the scalar curvature remains non-negative by Ricci flow and blows up in a short time.
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참고문헌 (14)
참고문헌 신청
B. Bidabad / 2014 / On quasi-Einstein Finsler spaces / Bull. Iranian Math. Soc 40 (4) : 921 ~ 930
B. Bidabad / 2015 / On compact Ricci solitons in Finsler geometry / C. R. Math. Acad. Paris 353 (11) : 1023 ~ 1027
B. Bidabad / 2016 / Convergence of Finslerian metrics under Ricci ow / Sci. China Math 59 (4) : 741 ~ 750
B. Chow / 2004 / The Ricci Flow: An Introduction / AMS
B. Shen / 2016 / Twisted Ricci ow on a class of Finsler metrics and its solitons / Differential Geom. Appl 46 : 132 ~ 145
B. Bidabad / 2015 / On compact Ricci solitons in Finsler geometry / C. R. Math. Acad. Paris 353 (11) : 1023 ~ 1027
B. Bidabad / 2016 / Convergence of Finslerian metrics under Ricci ow / Sci. China Math 59 (4) : 741 ~ 750
B. Chow / 2004 / The Ricci Flow: An Introduction / AMS
B. Shen / 2016 / Twisted Ricci ow on a class of Finsler metrics and its solitons / Differential Geom. Appl 46 : 132 ~ 145
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