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In this paper we study the Myers' theorem for orientable Riemannian hypersurfaces under some restrictions on the mean curvature, the second-order mean curvature, or the divergence of the shape operator and give some estimates for the diameter of such hypersurfaces.
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참고문헌 (13)
참고문헌 신청
L. J. Alꠕas / 2016 / Maximum principles and geometric applica-tions / Springer
M. P. Cavalcante / 2015 / Compactness in Weighted Manifolds and Applications / Results in Mathematics 68(1-2):143~156
F. Fang / 2009 / Two generalizations of Cheeger-Gromoll splitting theorem via Bakry-Emery Ricci curvature / Ann. Inst. Fourier (Grenoble) 59(2):563~573
Akito Futaki / 2013 / On the first eigenvalue of the Witten–Laplacian and the diameter of compact shrinking solitons / Annals of Global Analysis and Geometry 44(2):105~114
Xiang-Dong Li / 2005 / Liouville theorems for symmetric diffusion operators on complete Riemannian manifolds / Journal de Mathématiques Pures et Appliquées 84(10):1295~1361
M. P. Cavalcante / 2015 / Compactness in Weighted Manifolds and Applications / Results in Mathematics 68(1-2):143~156
F. Fang / 2009 / Two generalizations of Cheeger-Gromoll splitting theorem via Bakry-Emery Ricci curvature / Ann. Inst. Fourier (Grenoble) 59(2):563~573
Akito Futaki / 2013 / On the first eigenvalue of the Witten–Laplacian and the diameter of compact shrinking solitons / Annals of Global Analysis and Geometry 44(2):105~114
Xiang-Dong Li / 2005 / Liouville theorems for symmetric diffusion operators on complete Riemannian manifolds / Journal de Mathématiques Pures et Appliquées 84(10):1295~1361
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