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On Finsler metrics of constant S-curvature

Xiaohuan Mo|Xiaoyang Wang
대한수학회 (The Korean Mathematical Society)|2013.03|대한수학회보 (Bulletin of the KMS)|제50권 제2호|pp. 639-648

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참고문헌

키워드

existenceFinsler metricβ)-metric(αS-curvatureH-curva- ture
주제분류수학

초록

In this paper, we study Finsler metrics of constant S-curva- ture. First we produce infinitely many Randers metrics with non-zero (constant) S-curvature which have vanishing H-curvature. They are counterexamples to Theorem 1.2 in [20]. Then we show that the existence of (α, β)-metrics with arbitrary constant S-curvature in each dimension which is not Randers type by extending Li-Shen’ construction.

Abstract

In this paper, we study Finsler metrics of constant S-curva- ture. First we produce infinitely many Randers metrics with non-zero (constant) S-curvature which have vanishing H-curvature. They are counterexamples to Theorem 1.2 in [20]. Then we show that the existence of (α, β)-metrics with arbitrary constant S-curvature in each dimension which is not Randers type by extending Li-Shen’ construction.

참고문헌 (20)

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  12. B. Najafi, "Finsler metrics of scalar flag curvature with special non-Riemannian curvature properties", Geom. Dedicata, 131, pp.87~97 (2008)
  13. S. Ohta, "Vanishing S-curvature of Randers spaces", Differential Geom. Appl, 29(2), pp.174~178 (2011)
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  16. Z. Shen, "Projectively flat Randers metrics with constant flag curvature", Math. Ann, 325(1), pp.19~30 (2003)
  17. Z. Shen, "Landsberg curvature, S-curvature and Riemann curvature, A sampler of Riemann-Finsler geometry, In Math. Sci. Res. Inst. Publ., 50", pp.303~355 (2004), Cambridge Univ. Press
  18. Z. Shen, "Finsler manifolds with nonpositive flag curvature and constant S-curvature", Math. Z, 249(3), pp.625~639 (2005)
  19. Z. Shen, "On some non-Riemannian quantities in Finsler geometry", Cana. Math. Bull, 56, pp.184~193 (2013)
  20. D. Tang, "On the non-Riemannian quantity H in Finsler geometry", Differential Geom. Appl, 29(2), pp.207~213 (2011)

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