y − x ≥ v(y) − v(x) d − h ≥ b + |M n | 2 − 1 a − 1 ≥ b 2 − 1 a − 1 in this case as well. Again, the unboundedness of D(v, M) follows.
We completely classify constant mean curvature hypersurfaces (CMC) with constant δ-invariant in the unit 4-sphere S 4 and in the Euclidean 4-space E 4 .
We present a method to construct a large family of Lagrangian surfaces in complex Euclidean plane C 2 by using Legendre curves in the 3-sphere and in the anti de Sitter 3-space or, equivalently, by using spherical and hyperbolic curves, respectively. Among this family, we characterize minimal, constant mean curvature, Hamiltonian-minimal and Willmore… (More)
A new geometric invariant will be introduced, studied and determined on compact symmetric spaces. Introduction. We will introduce a new invariant on Riemannian manifolds, which is especially interesting on compact symmetric spaces, and we will determine the invariant for the compact symmetric spaces, thus amplifying the announcement
Lagrangian //-umbilical submanifolds are the "simplest" Lagrangian submanifolds next to totally geodesic ones in complex-space-forms. The class of Lagrangian //-umbilical submanifolds in complex Euclidean spaces includes Whitney's spheres and Lagrangian pseudo-spheres. For each submanifold M of Euclidean «-space and each unit speed curve F in the complex… (More)
OBJECTIVE To elucidate the effect of Chinese herbal medicine (CHM) for nourishing Yin and removing fire on the biosynthesis, secretion and regulative mechanism of gonadotropin-releasing hormone (GnRH) in hypothalamus. METHODS The brain slices of medial basal hypothalamus of adolescent rats, which had been fed with CHM, were incubated. The content of GnRH… (More)
Einstein manifolds are trivial examples of gradient Ricci soli-tons with constant potential function and thus they are called trivial Ricci solitons. In this paper, we prove two characterizations of compact shrinking trivial Ricci solitons.
A production function f is called quasi-sum if there are continuous strict monotone functions F, h 1 ,. .. , hn with F > 0 such that f (x) = F (h 1 (x 1) + · · · + hn(xn)) (cf. ). A quasi-sum production function is called quasi-linear if at most one of F, h 1 ,. .. , hn is a nonlinear function. For a production function f , the graph of f is called the… (More)