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초록· 키워드
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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.
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참고문헌 (10)
참고문헌 신청
E AUBRY / 2007 / Finiteness of π1π1 and geometric inequalities in almost positive Ricci curvature / Annales Scientifiques de l’École Normale Supérieure 40(4):675~695
D. Bao / 2000 / An introduction to Riemann-Finsler geometry / Springer-Verlag
Carmen Chicone / 1980 / Line integration of Ricci curvature and conjugate points in Lorentzian and Riemannian manifolds / Manuscripta Mathematica 31(1-3):297~316
P. Petersen / 1998 / Integral curvature bounds, distance estimates and appli-cations / J. Dierential Geom 50(2):269~298
YiBing Shen / 2011 / On fundamental groups of Finsler manifolds / Science China Mathematics 54(9):1951~1964
D. Bao / 2000 / An introduction to Riemann-Finsler geometry / Springer-Verlag
Carmen Chicone / 1980 / Line integration of Ricci curvature and conjugate points in Lorentzian and Riemannian manifolds / Manuscripta Mathematica 31(1-3):297~316
P. Petersen / 1998 / Integral curvature bounds, distance estimates and appli-cations / J. Dierential Geom 50(2):269~298
YiBing Shen / 2011 / On fundamental groups of Finsler manifolds / Science China Mathematics 54(9):1951~1964
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