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Search: All articles in the CMB digital archive with keyword Ricci curvature

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1. CMB 2015 (vol 58 pp. 787)

 Non-branching RCD$(0,N)$ Geodesic Spaces with Small Linear Diameter Growth have Finitely Generated Fundamental Groups In this paper, we generalize the finite generation result of Sormani to non-branching $RCD(0,N)$ geodesic spaces (and in particular, Alexandrov spaces) with full support measures. This is a special case of the Milnor's Conjecture for complete non-compact $RCD(0,N)$ spaces. One of the key tools we use is the Abresch-Gromoll type excess estimates for non-smooth spaces obtained by Gigli-Mosconi. Keywords:Milnor conjecture, non negative Ricci curvature, curvature dimension condition, finitely generated, fundamental group, infinitesimally HilbertianCategories:53C23, 30L99

2. CMB 2015 (vol 58 pp. 530)

Li, Benling; Shen, Zhongmin
 Ricci Curvature Tensor and Non-Riemannian Quantities There are several notions of Ricci curvature tensor in Finsler geometry and spray geometry. One of them is defined by the Hessian of the well-known Ricci curvature. In this paper we will introduce a new notion of Ricci curvature tensor and discuss its relationship with the Ricci curvature and some non-Riemannian quantities. By this Ricci curvature tensor, we shall have a better understanding on these non-Riemannian quantities. Keywords:Finsler metrics, sprays, Ricci curvature, non-Riemanian quantityCategories:53B40, 53C60

3. CMB 2014 (vol 58 pp. 158)

 Corrigendum to "Chen Inequalities for Submanifolds of Real Space Forms with a Semi-symmetric Non-metric Connection" We fix the coefficients in the inequality (4.1) in the Theorem 4.1(i) from A. Mihai and C. ÃzgÃ¼r, "Chen inequalities for submanifolds of real space forms with a semi-symmetric non-metric connection" Canad. Math. Bull. 55 (2012), no. 3, 611-622. Keywords:real space form, semi-symmetric non-metric connection, Ricci curvatureCategories:53C40, 53B05, 53B15

4. CMB 2011 (vol 55 pp. 611)

 Chen Inequalities for Submanifolds of Real Space Forms with a Semi-Symmetric Non-Metric Connection In this paper we prove Chen inequalities for submanifolds of real space forms endowed with a semi-symmetric non-metric connection, i.e., relations between the mean curvature associated with a semi-symmetric non-metric connection, scalar and sectional curvatures, Ricci curvatures and the sectional curvature of the ambient space. The equality cases are considered. Keywords:real space form, semi-symmetric non-metric connection, Ricci curvatureCategories:53C40, 53B05, 53B15

5. CMB 2006 (vol 49 pp. 152)

Yun, Jong-Gug
 Comparison Geometry With\\$L^1$-Norms of Ricci Curvature We investigate the geometry of manifolds with bounded Ricci curvature in $L^1$-sense. In particular, we generalize the classical volume comparison theorem to our situation and obtain a generalized sphere theorem. Keywords:Mean curvature, Ricci curvatureCategory:53C20

6. CMB 2004 (vol 47 pp. 314)

Yun, Jong-Gug
 Mean Curvature Comparison with $L^1$-norms of Ricci Curvature We prove an analogue of mean curvature comparison theorem in the case where the Ricci curvature below a positive constant is small in $L^1$-norm. Keywords:mean curvature, Ricci curvatureCategory:53C20

7. CMB 1999 (vol 42 pp. 214)

Paeng, Seong-Hun; Yun, Jong-Gug
 Conjugate Radius and Sphere Theorem Bessa [Be] proved that for given $n$ and $i_0$, there exists an $\varepsilon(n,i_0)>0$ depending on $n,i_0$ such that if $M$ admits a metric $g$ satisfying $\Ric_{(M,g)} \ge n-1$, $\inj_{(M,g)} \ge i_0>0$ and $\diam_{(M,g)} \ge \pi-\varepsilon$, then $M$ is diffeomorphic to the standard sphere. In this note, we improve this result by replacing a lower bound on the injectivity radius with a lower bound of the conjugate radius. Keywords:Ricci curvature, conjugate radiusCategories:53C20, 53C21
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