1. CMB Online first
 Li, Benling; Shen, Zhongmin

Ricci Curvature Tensor and NonRiemannian 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 wellknown 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
nonRiemannian quantities. By this Ricci curvature tensor, we shall
have a better understanding on these nonRiemannian quantities.
Keywords:Finsler metrics, sprays, Ricci curvature, nonRiemanian quantity Categories:53B40, 53C60 

2. CMB 2014 (vol 58 pp. 158)
3. CMB 2011 (vol 55 pp. 611)
 Özgür, Cihan; Mihai, Adela

Chen Inequalities for Submanifolds of Real Space Forms with a SemiSymmetric NonMetric Connection
In this paper we prove Chen inequalities for submanifolds of real space
forms endowed with a semisymmetric nonmetric connection, i.e., relations
between the mean curvature associated with a semisymmetric nonmetric
connection, scalar and sectional curvatures, Ricci curvatures and the
sectional curvature of the ambient space. The equality cases are considered.
Keywords:real space form, semisymmetric nonmetric connection, Ricci curvature Categories:53C40, 53B05, 53B15 

4. CMB 2006 (vol 49 pp. 152)
5. CMB 2004 (vol 47 pp. 314)
6. CMB 1999 (vol 42 pp. 214)
 Paeng, SeongHun; Yun, JongGug

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 $\Ric_{(M,g)} \ge n1$, $\inj_{(M,g)}
\ge i_0>0$ 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 
