pseudo ricci symmetric real hypersurfaces of a complex projective space are classified and it is proved that there are no pseudo ricci symmetric real hypersurfaces of the complex projective space cpn for which the vector field ξ from the almost contact metric structure (φ, ξ, η, g) is a principal curvature vector field.

An automatic polyp detection framework is presented based on surface curvatures, and a new color coding scheme is used to highlight the detected polyps which enhances the visualization. An accurate estimate for the surface curvature together with three geometric features is used to detect the polyps. We place the detected polyps inside a polygonal dataset with exactly the same topology and geom...

In this paper are determined the principal curvatures and principal curvature lines on canal surfaces which are the envelopes of families of spheres with variable radius and centers moving along a closed regular curve in R3. By means of a connection of the differential equations for these curvature lines and real Riccati equations, it is established that canal surfaces have at most two isolated...

In this paper are determined the principal curvatures and principal curvature lines on canal surfaces which are the envelopes of families of spheres with variable radius and centers moving along a closed regular curve in R. By means of a connection of the differential equations for these curvature lines and real Riccati equations, it is established that canal surfaces have at most two isolated ...

Surface creases provide us with important information about the shapes of objects and can be intuitively defined as curves on a surface along which the surface bends sharply. Our mathematical description of such surface creases is based on study of extrema of the principal curvatures along their curvature lines. On a smooth generic surface we define ridges to be the local positive maxima of the...

In this paper we study the pairs of orthogonal foliations on oriented surfaces immersed in R3 whose singularities and leaves are, respectively, the umbilic points and the lines of normal mean curvature of the immersion. Along these lines the immersions bend in R3 according to their normal mean curvature. By analogy with the closely related Principal Curvature Configurations studied in [S-G], [G...

The primary objective of this study was to quantitatively investigate the human perception of surface curvature by using virtual surfaces and motor tasks along with data analysis methods to estimate surface curvature from drawing movements. Three psychophysical experiments were conducted. In Experiment 1, we looked at subjects' sensitivity to the curvature of a curve lying on a surface and chan...

This paper addresses the numerical estimation of the principal curvature of pattern transformation manifolds. When a visual pattern undergoes a geometric transformation, it forms a (sub)manifold in the ambient space, which is usually called the transformation manifold. The manifold curvature is an important property characterizing the manifold geometry, with several applications in manifold lea...

Chen's biharmonic conjecture is well-known and stays open: The only biharmonic submanifolds of Euclidean spaces are the minimal ones. In this paper, we consider an advanced version of the conjecture, replacing $Delta$ by its extension, $L_1$-operator ($L_1$-conjecture). The $L_1$-conjecture states that any $L_1$-biharmonic Euclidean hypersurface is 1-minimal. We prove that the $L_1$-conje...

We present a new way to compute the aane curvature of plane curves. We explain how an aane scale-space can be used to gain one order of derivation in the numerical approximation of aane curvature. We outline our implementation and compare our results with previous ones. This paper ends by showing a simple application in pattern recognition using aane curvature.