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1. 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 curvature Categories:53C40, 53B05, 53B15 |
2. CMB 2006 (vol 49 pp. 152)
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 curvature Category:53C20 |
3. CMB 2004 (vol 47 pp. 314)
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 curvature Category:53C20 |
4. CMB 1999 (vol 42 pp. 214)
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 radius Categories:53C20, 53C21 |