논문KCI 등재
Generalized Myers theorem for Finsler manifolds with integral Ricci curvature bound
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
주제분류수학
초록
We establish the generalized Myers theorem for Finsler manifolds under integral Ricci curvature bound. More precisely, we show that the forward complete Finsler $n$-manifold whose part of Ricci curvature less than a positive constant is small in $L^p$-norm (for $p>n/2$) have bounded diameter and finite fundamental group.
Abstract
We establish the generalized Myers theorem for Finsler manifolds under integral Ricci curvature bound. More precisely, we show that the forward complete Finsler $n$-manifold whose part of Ricci curvature less than a positive constant is small in $L^p$-norm (for $p>n/2$) have bounded diameter and finite fundamental group.
참고문헌 (10)
- E AUBRY, "Finiteness of π1π1 and geometric inequalities in almost positive Ricci curvature", Annales Scientifiques de l’École Normale Supérieure, 40(4), pp.675~695 (2007), Societe Mathematique de France[DOI]
- D. Bao, "An introduction to Riemann-Finsler geometry" (2000), Springer-Verlag
- Carmen Chicone, "Line integration of Ricci curvature and conjugate points in Lorentzian and Riemannian manifolds", Manuscripta Mathematica, 31(1-3), pp.297~316 (1980), Springer Science and Business Media LLC[DOI]
- P. Petersen, "Integral curvature bounds, distance estimates and appli-cations", J. Dierential Geom, 50(2), pp.269~298 (1998)[DOI]
- YiBing Shen, "On fundamental groups of Finsler manifolds", Science China Mathematics, 54(9), pp.1951~1964 (2011), Springer Science and Business Media LLC[DOI]
- BING YE WU, "Volume form and its applications in Finsler geometry", Publicationes Mathematicae Debrecen, 78(3-4), pp.723~741 (2011), University of Debrecen[DOI]
- B. Y. WU, "ON INTEGRAL RICCI CURVATURE AND TOPOLOGY OF FINSLER MANIFOLDS", International Journal of Mathematics, 23(11), pp.1250111~ (2012), World Scientific Pub Co Pte Lt[DOI]
- Bing-Ye Wu, "A note on the generalized Myers theorem for Finsler manifolds", 대한수학회보, 50(3), pp.833~837 (2013), 대한수학회
- B.-Y. Wu, "Comparison Theorems and Submanifolds in Finsler Geometry" (2015), Science Press
- Jong-Gug Yun, "A note on the generalized Myers theorem", 대한수학회보, 46(1), pp.61~66 (2009), 대한수학회
관련 논문AI추천
A note on the generalized Myers theorem for Finsler manifoldsBing-Ye Wu대한수학회 · 대한수학회보2013 · 제50권 제3호Comparison theorems in Riemann-Finsler geometry with line radial integral curvature bounds and related resultsBing-Ye Wu대한수학회 · 대한수학회지2019 · 제56권 제2호COMPARISON THEOREMS IN FINSLER GEOMETRY WITH WEIGHTED CURVATURE BOUNDS AND RELATED RESULTSBing-Ye Wu대한수학회 · 대한수학회지2015 · 제52권 제3호Harmonic Finsler manifolds with minimal horospheres김창완대한수학회 · 대한수학회논문집2018 · 제33권 제3호Weighted Poincar\'e inequality and its applications on Finsler manifolds대한수학회 · 대한수학회보2026 · 제63권 제1호Rigidity theorems of some dually flat Finsler metrics and its applicationsBin Shen, Yanfang Tian대한수학회 · 대한수학회보2016 · 제53권 제5호
이 간행물의 다른 논문 (17건)
On the denominator of Dedekind sumsSt'ephane R. Louboutinpp. 815-827Weakly prime ideals in commutative semigroupsD. D. Anderson, Jason R. Juett, 천상민pp. 829-839Gradient estimates of a nonlinear elliptic equation for the $V$-LaplacianFanqi Zengpp. 853-865Geometric characterizations of canal surfaces in Minkowski 3-space $\mathbb{I}$Mengfei Su, 부설산, Jinhua Qian, 정승달pp. 867-883A note on the first order commutator $\mathcal{C}_2$Wenjuan Li, Suying Liupp. 885-898