A del Pezzo manifold is a projective manifold X of dimension n whose anticanonical bundle is ample and divisible by n−1 in the Picard group. These manifolds are classical objects in algebraic geometry and completely classified (Iskovskikh, Fujita, ...). In terms of differential geometry one classifies manifolds with positive Ricci curvature whose canonical class has the above divisibility. It i...

Precise segmentation of underlying objects in an image is very important especially for biomedical image analysis. Here, we present an integrated approach for boundary nding using region and curvature information along with the gradient. Unlike the previous methods , where smoothing is enforced by penalizing curvature , here the grey level curvature is used as an extra source of information. Ho...

This work is devoted to the Lipschitz contraction and the long time behavior of certain Markov processes. These processes diffuse and jump. They can represent some natural phenomena like size of cell or data transmission over the Internet. Using a Feynman-Kac semigroup, we prove a bound in Wasserstein metric. This bound is explicit and optimal in the sense of Wasserstein curvature. This notion ...

In this paper is studied the behavior of principal curvature lines near a curve of umbilic points of a smooth surface.

in this paper, the time-like hyperruled surfaces in the minkowski 4-space and their algebraicinvariants are worked. also some characteristic results are found about these algebraic invariants.

‎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...

The simplest patterns of qualitative changes on the configurations of lines of principal curvature around umbilic points on surfaces whose immersions into R3 depend smoothly on a real parameter (codimension one umbilic bifurcations) are described in this paper. Global effects, due to umbilic bifurcations, on these configurations such as the appearance and annihilation of periodic principal line...

We give a complete characterization of invariant integrable complex structures on principal bundles defined over hermitian symmetric spaces, using the Jordan algebraic approach for the curvature computations. In view of possible generalizations, the general setup of invariant holomorphic principal fibre bundles is described in a systematic way.