In this paper‎, ‎the‎ ‎authors prove that a strictly Kähler-Berwald manifold with‎ ‎nonzero constant holomorphic sectional curvature must be a‎ Kähler manifold‎. 

where H(x, t) is the mean curvature vector of Ft(M) and Ft(x) = F (x, t). We call F : M × [0, T ) → F(c) the mean curvature flow with initial value F . The mean curvature flow was proposed by Mullins [17] to describe the formation of grain boundaries in annealing metals. In [3], Brakke introduced the motion of a submanifold by its mean curvature in arbitrary codimension and constructed a genera...

A direct, bundle-theoretic method for defining and extending local isometries out of curvature data is developed. As a by-product, conceptual direct proofs of a classical result of Singer and a recent result of the authors are derived. A classical result of I. M. Singer [11] states that a Riemannian manifold is locally homogeneous if and only if its Riemannian curvature tensor together with its...

We investigated whether observers use rate of change of curvature in visually extrapolating contour shape. Arcs of Euler spirals with positive or negative rate of change of curvature gamma (hence linearly increasing or decreasing curvature) disappeared behind the straight-edge of a half-disk occluder. Observers adjusted the position and the orientation of a line probe around the curved portion ...

Consider a Riemannian manifold with bounded Ricci curvature $|\mathrm{Ric}|\leq n-1$ and the noncollapsing lower volume bound $\mathrm{Vol}(B_1(p))>\mathrm{v}>0$. The first main result of this paper is to prove that we have $L^2$ $⨏_{B_1(p)}|\mathrm{Rm}|^2(x)\, dx \lt C(n,\mathrm{v})$,which proves conjecture. In order this, will need show following structural for limits. Namely, if $(M^n_j,d_j,...

Membrane curvature is no longer seen as a passive consequence of cellular activity but an active means to create membrane domains and to organize centres for membrane trafficking. Curvature can be dynamically modulated by changes in lipid composition, the oligomerization of curvature scaffolding proteins and the reversible insertion of protein regions that act like wedges in membranes. There is...

it is easily seen that a motion and a homothetic transformation are both affine collineations and that an affine collineation preserves the curvature tensor. In [l ] one of the present authors proved that in a space of nonzero constant curvature a mapping preserving curvature is a motion. For an Einstein space with nonzero curvature scalar, a mapping preserving Ricci curvature is a motion; for ...

Until now, the genomic DNA of all eubacteria analyzed has been hyper-curved, its global intrinsic curvature being higher than that of a random sequence. In contrast, that rule failed for archaea or eukaryotes, which could be either hypo- or hyper-curved. The existence of the rule suggested that, at least for eubacteria, global intrinsic curvature is adaptive. However, the present results from a...

Phototropic and gravitropic curvature by hypocotyls of Arabidopsis thaliana is minimal when the side of the hook with the cotyledons attached is positioned toward the direction of tropistic curvature, and maximal when that side of the hook is positioned away from the direction of tropistic curvature. Based on these data, it is proposed that the position of the hook with attached cotyledons aff...