in this paper, by modifying cheng-yau$'$s technique to complete hypersurfaces in $s^{n+1}(1)$, we prove a rigidity theorem under the hypothesis of the mean curvature and the normalized scalar curvature being linearly related which improve the result of [h. li, hypersurfaces with constant scalar curvature in space forms, {em math. ann.} {305} (1996), 665--672].

Let Mn be a Riemannian n-manifold. Denote by S(p) and Ric(p) the Ricci tensor and the maximum Ricci curvature on Mn, respectively. In this paper we prove that every C-totally real submanifolds of a Sasakian space form M̄2m+1(c) satisfies S ≤ ( (n−1)(c+3) 4 + n 2 4 H2)g, where H2 and g are the square mean curvature function and metric tensor on Mn, respectively. The equality holds identically if ...

‎The object of the present paper is to study spacetimes admitting‎ ‎quasi-conformal curvature tensor‎. ‎At first we prove that a quasi-conformally flat spacetime is Einstein‎ ‎and hence it is of constant curvature and the energy momentum tensor of such a spacetime satisfying‎ ‎Einstein's field equation with cosmological constant is covariant constant‎. ‎Next‎, ‎we prove that if the perfect flui...

Hillslopes have complex three-dimensional shapes that are characterized by their plan shape, profile curvature of surface and bedrock, and soil depth. To investigate the stability of complex hillslopes (with different slope curvatures and plan shapes), we combine the hillslopestorage Boussinesq (HSB) model with the infinite slope stability method. The HSB model is based on the continuity and Da...

Background: Scoliosis is a health problem that causes a side-to-side curvature in the spine. The curvature may have an “S” or “C” shape. To evaluate scoliosis, the Cobb angle has been commonly used. However, digital image processing allows the Cobb angle to be obtained easily and quickly, several researchers have determined that Cobb angle contains high variations (errors) in the measurements. ...

An experimental study of time-dependent Bénard-Marangoni convection in small aspect ratio containers and high Prandtl number fluids is presented. Two similar systems with the same aspect ratio, depth, and type of fluid are compared: one with adiabatic lateral boundaries and the other with open boundaries. In spite of the fact that very different plan forms and flows appear, both systems exhibit...

we establish some relative volume comparison theorems for extremal volume forms of‎ ‎finsler manifolds under suitable curvature bounds‎. ‎as their applications‎, ‎we obtain some results on curvature and topology of finsler manifolds‎. ‎our results remove the usual assumption on s-curvature that is needed in the literature‎.

In this paper, we have developed a digital atlas of the pediatric human brain. Human brain atlases, used to visualize spatially complex structures of the brain, are indispensable tools in model-based segmentation and quantitative analysis of brain structures. However, adult brain atlases do not adequately represent the normal maturational patterns of the pediatric brain, and the use of an adult...