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].  

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 many everyday situations, we bias our perception from the top down, based on a task or an agenda. Frequently, this entails shifting attention to a specific attribute of a particular object or scene. To explore the cost of shifting top-down attention to a different stimulus attribute, we adopt the task-set switching paradigm, in which switch trials are contrasted with repeat trials in mixed-t...

‎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...

recently, we have used the symmetric bracket of vector fields, and developed the notion of the symmetric derivation. using this machinery, we have defined the concept of symmetric curvature. this concept is natural and is related to the notions divergence and laplacian of vector fields. this concept is also related to the derivations on the algebra of symmetric forms which has been discus...

in this paper, we obtain two intrinsic integral inequalities of hessian manifolds.

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].