Let (M,gTM) be a noncompact (not necessarily complete) enlargeable Riemannian manifold in the sense of Gromov-Lawson and F an integrable subbundle TM. kF leafwise scalar curvature associated to gF=gTM|F. We show that if either TM or is spin, then inf(kF)≤0. This generalizes famous result on manifolds case foliations. It also extends ansatz Gromov hyper-Euclidean spaces general manifolds, as wel...

A subbundle of variable dimension inside the tangent bundle of a smooth manifold is called a smooth distribution if it is the pointwise span of a family of smooth vector fields. We prove that all such distributions are finitely generated, meaning that the family may be taken to be a finite collection. Further, we show that the space of smooth sections of such distributions need not be finitely ...

We apply the notion of foliation to a nonholonomic manifold, which was introduced for geometric interpretation constrained systems in mechanics. prove series integral formulas foliated sub-Riemannian that is, Riemannian manifold equipped with distribution $${{\mathscr {D}}}$$ and {F}}}$$ whose tangent bundle is subbundle . Our generalize some results involve shape operators $${\mathscr {F}}$$ r...

In Finsler geometry, the notion of parallel for Finsler tensor fields is defined, already. In this paper, however, for vector fields on a base manifold, the author studies the notion of parallel. In the last section, the obtained results are shown as compare corresponding properties to them of Riemannian geometry. Introduction The author gave the definition (1.1) of the parallel displacement al...

Examples of Kähler metrics of constant scalar curvature are relatively scarce. Over the past two decades, several workers in geometry and physics have used symmetry reduction to construct complete Kähler metrics of constant scalar curvature by ODE methods. One fruitful idea—the “Calabi ansatz”—is to begin with an Hermitian line bundle p : (L, h)→ (M, gM ) over a Kähler manifold, and to search f...

An ionic current model of the retinal horizontal cell is constructed. The horizontal cell models are interconnected by gap junctions to form a horizontal cell layer. The light response properties of the L-type horizontal cell are analyzed using this model. We demonstrate the functional role of each ionic current and the role of the feedback loop between cones and horizontal cells. The present s...

We describe a stochastic birth-and-death model of evolution of horizontally transferred genes in microbial populations. The model is a generalization of the stochastic model described by Berg and Kurland and includes five parameters: the rate of mutational inactivation, selection coefficient, invasion rate (i.e., rate of arrival of a novel sequence from outside of the recipient population), wit...

Motivated by the analogies between the projective and the almost quaternionic geometries, we first study the generalized planar curves and mappings. We follow, recover, and extend the classical approach, see e.g. [9, 10]. Then we exploit the impact of the general results in the almost quaternionic geometry. In particular we show, that the natural class of H–planar curves coincides with the clas...

Let M be a C∞ Riemannian manifold, dimM = n. A distribution on M is a smooth linear subbundle of the tangent bundle TM . We denote by q the fiber of at q ∈M ; q ⊂ TqM . The number k = dim q is the rank of the distribution. We assume that 1 < k < n. The restriction of the Riemannian structure to is a sub-Riemannian structure. Lipschitz integral curves of the distribution are called admissible pa...