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].

PURPOSE To explore the potential effect of ageing on the corneal curvature and corrected visual acuity in patients with long-term keratoconus because of the paucity of these patients older than 50 years. METHODS Records of keratoconic patients, who had initially presented to a specialized contact lens clinic and followed for more than 20 years after disease onset, were reviewed. Collected inf...

The accurate detection of static object boundaries such as contours or surfaces and dynamic tunnels of moving objects via deformable models is an ongoing research topic in computer vision. Most deformable models attempt to converge towards a desired solution by minimizing the sum of internal (prior) and external (measurement) energy terms. Such an approach is elegant, but frequently mis-converg...

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 measurement of distance between two objects is generalized to the case where the objects are no longer points but are one-dimensional. Additional concepts such as nonextensibility, curvature constraints, and noncrossing become central to the notion of distance. Analytical and numerical results are given for some specific examples, and applications to biopolymers are discussed.

‎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...

In this work, we discuss an optical method for measuring surface tension induced menisci. The principle of measurement is based upon the change in the background pattern produced by the curvature of the meniscus acting as a lens. We measure the meniscus profile over an inclined glass plate and utilize the measured meniscus for estimation of surface tension and refractive index.