in this paper, we obtain a necessary and sufficient condition for a conformal mapping between two weyl manifolds to preserve einstein tensor. then we prove that some basic curvature tensors of $w_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. also, we obtained the relation between the scalar curvatures of the weyl manifolds r...

Local curvature represents an important shape parameter of space curves which are well described by differential geometry. We have developed an estimator for local curvature of space curves embedded in nD grey-value images. There is neither a segmentation of the curve needed nor a parametric model assumed. Our estimator works on the orientation field of the space curve. This orientation field a...

On the mean curvature of a unit vector field. Abstract We present an explicit formula for the mean curvature of a unit vector field on a Riemannian manifold, using a special but natural frame. As applications, we treat some known and new examples of minimal unit vector fields. We also give an example of a vector field of constant mean curvature on the Lobachevsky (n + 1) space.

The aim of this paper is to characterize $3$-dimensional $N(k)$-paracontact metric manifolds satisfying certain curvature conditions. We prove that a $3$-dimensional $N(k)$-paracontact metric manifold $M$ admits a Ricci soliton whose potential vector field is the Reeb vector field $xi$ if and only if the manifold is a paraSasaki-Einstein manifold. Several consequences of this result are discuss...

The definition of mass of a scalar field in a curved space has often been generalized by grouping coupling terms between the field and the Ricci curvature with non–curvature–related mass terms. In a broader point of view, one sees that a common misunderstanding resulting from such an identification leads one, in the case of the spin 2 field, to regard the cosmological constant as a non–vanishin...

We present coarse-grained molecular dynamics simulations of the epsin N-terminal homology domain interacting with a lipid bilayer and demonstrate a rigorous theoretical formalism and analysis method for computing the induced curvature field in varying concentrations of the protein in the dilute limit. Our theory is based on the description of the height-height undulation spectrum in the presenc...

‎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...

For submanifolds tangent to the structure vector field in Sasakian space forms, we establish a Chen’s basic inequality between the main intrinsic invariants of the submanifold namely, its pseudosectional curvature and pseudosectional curvature on one side and the main extrinsic invariant namely, squared pseudomean curvature on the other side with respect to the TanakaWebster connection. Moreove...