Ambrose Teoreminin Finsler Versiyonu Üzerine Bir Not

Year 2020, , 1108 - 1114, 26.09.2020

Yasemin Soylu

https://doi.org/10.17798/bitlisfen.665977

Abstract

(ℵ,F) manifoldu forward tam, bağlantılı ve n≥2 boyutlu bir Finsler manifold olsun. Bu çalışmada, Riemann manifoldlarında elde edilen Ambrose kompaktlık teoremi, ağırlıklı Ricci eğriliği kullanılarak Finsler manifoldlara genişletilmiştir. İstenilen sonuçların kanıtları için Bochner Weitzenböck formülü ve uygun dizi seçimleri kullanılmıştır.

Keywords

: Finsler manifold, S-eğriliği, ağırlıklı Ricci eğriliği

A Note on Finsler Version of Ambrose Theorem

Abstract

Let (ℵ,F) be a forward complete and connected Finsler manifold of dimensional n≥2. In this study, we extend Ambrose’s compactness theorem in Riemannian manifolds to Finsler manifolds by using the weighted Ricci curvature. We use the Bochner Weitzenböck formula and suitable sequence choices for the proofs of the desired results.

Keywords

Finsler Manifold, S-curvature, weighted Ricci curvature

References

• 1. Ohta S. 2009. Finsler interpolation inequalities. Calc. Var. Partial Differ. Equ., 36: 211-249.
• 2. Wu B. 2013. A note on the generalized Myers theorem for Finsler manifolds. Bull. Korean Math. Soc., 50: 833–837.
• 3. Yin S. 2017. Two compactness theorems on Finsler manifolds with positive weighted Ricci curvature. Results Math., 72: 319–327.
• 4. Ambrose W. 1957. A theorem of Myers. Duke Math. J., 24: 345–348.
• 5. Anastasiei M. 2015. Galloway’s compactness theorem on Finsler manifolds. Balkan J. Geom. Appl., 20: 1–8.
• 6. Kim C.-W. 2017. On Existence and Distribution of Conjugate Points in Finsler Geometry. J. Chungcheong Math. Soc., 30: 369–379.
• 7. Galloway G. J. 1982. Compactness criteria for Riemannian manifolds. Proc. Amer. Math. Soc., 84: 106–110.
• 8. Zhang S. 2014. A theorem of Ambrose for Bakry-Emery Ricci tensor. Ann. Glob. Anal. Geom., 45: 233–238.
• 9. Cavalcante M.P., Oliveira J.Q., Santos M.S. 2015. Compactness in weighted manifolds and applications. Results Math., 68: 143–156.
• 10. Wu B., Xin Y. 2007. Comparison theorems in Finsler geometry and their applications. Math. Ann., 337: 177–196.
• 11. Shen Z. 2001. Lectures on Finsler Geometry. World Scientific, Singapore.
• 12. Ohta S., Sturm K.-T. 2014. Bochner-Weitzenböck formula and Li-Yau estimates on Finsler manifolds. Adv. Math., 252: 429–448.