Direct measurement of the curvature of visual space.

Gingival Thickness Assessment: Visual versus Direct Measurement

Background and Aim: Several methods have been suggested to measure gingival thick-ness. This study aimed to assess the reliability of visual assessment of facial gingival biotype of maxillary and mandibular teeth with or without using a periodontal probe in comparison with direct measurement. Materials and Methods: Sixty-seven healthy patients (25 women and 42 men) with a total of 100 hopele...

RICCI CURVATURE OF SUBMANIFOLDS OF A SASAKIAN SPACE FORM

Involving the Ricci curvature and the squared mean curvature, we obtain basic inequalities for different kind of submaniforlds of a Sasakian space form tangent to the structure vector field of the ambient manifold. Contrary to already known results, we find a different necessary and sufficient condition for the equality for Ricci curvature of C-totally real submanifolds of a Sasakian space form...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

‎Spacelike hypersurfaces with constant $S$ or $K$ in de Sitter‎ ‎space or anti-de Sitter space

‎Let $M^n$ be an $n(ngeq 3)$-dimensional complete connected and‎ ‎oriented spacelike hypersurface in a de Sitter space or an anti-de‎ ‎Sitter space‎, ‎$S$ and $K$ be the squared norm of the second‎ ‎fundamental form and Gauss-Kronecker curvature of $M^n$‎. ‎If $S$ or‎ ‎$K$ is constant‎, ‎nonzero and $M^n$ has two distinct principal‎ ‎curvatures one of which is simple‎, ‎we obtain some‎ ‎charact...

Probing the Probabilistic Effects of Imperfections on the Load Carrying Capacity of Flat Double-Layer Space Structures

Load carrying capacity of flat double-layer space structures majorly depends on the structures' imperfections. Imperfections in initial curvature, length, and residual stress of members are all innately random and can affect the load-bearing capacity of the members and consequently that of the structure. The double-layer space trusses are susceptible to progressive collapse due to sudden buckli...

Shape Operator of Slant Submanifolds in Kenmotsu Space Forms