We construct some natural metric connections on metric contact manifolds compatible with the contact structure and characterized by the Dirac operators they determine. In the case of CR manifolds these are invariants of a fixed pseudo-hermitian structure, and one of them coincides with the Tanaka–Webster connection.  2005 Elsevier B.V. All rights reserved. MSC: 53B05; 53C15; 53D10; 53D15

The problem of minimizing the cost functional of an Optimal Control System through the use of constrained Variational Calculus is a generalization of the geodetic problem in Riemannian geometry. In the framework of a geometric formulation of Optimal Control, we define a metric structure associated to the Optimal Control System on the enlarged space of state and time variables, such that the min...

in this paper, we study projective randers change and c-conformal change of p-reduciblemetrics. then we show that every p-reducible generalized landsberg metric of dimension n  2 must be alandsberg metric. this implies that on randers manifolds the notions of generalized landsberg metric andberwald metric are equivalent.

The study of metric fixed point theory has been researched extensively in the past decades, since fixed point theory plays a major role in mathematics and applied sciences, such as optimization, mathematical models, and economic theories. Different mathematicians tried to generalize the usual notion of metric space X, d such as Gähler 1, 2 andDhage 3–5 to extend knownmetric space theorems inmor...

Multi-task learning (MTL) has been shown to improve prediction performance in a number of different contexts by learning models jointly on multiple different, but related tasks. Network data, which are a priori data with a rich relational structure, provide an important context for applying MTL. In particular, the explicit relational structure implies that network data is not i.i.d. data. Netwo...

We assume that the manifold with boundary, X, has a SpinC-structure with spinor bundle S /. Along the boundary, this structure agrees with the structure defined by an infinite order integrable almost complex structure and the metric is Kähler. In this case the SpinC-Dirac operator ð agrees with ∂̄ + ∂̄∗ along the boundary. The induced CR-structure on bX is integrable and either strictly pseudocon...

Recall that a metric space M is said to be complete if every Cauchy sequence in M converges to a limit in M . Not all metric spaces are complete, but it is a fact that all metric spaces can be “completed”, in a way that preserves the essential structure of the metric space. If the space in question is a normed linear space this process completes the space to a Banach space, and an inner product...

We decribe a number of properties of a median metric space. In particular, we show that a complete connected median metric of finite rank admits a cononical bilipschitz equivalent CAT(0) metric. Metric spaces of this sort arise, up to bilipschitz equivalence, as asymptotic cones of certain classes of finitely generated groups, and the existence of such a structure has various consequences for t...

It is a fundamental fact that on an almost complex manifold with Hermitian metric (almost Hermitian manifold), the action of the almost complex structure on the tangent space at each point of the manifold is isometry. There is another kind of metric, called a Norden metric or a B-metric on an almost complex manifold, such that the action of the almost complex structure is anti-isometry with res...

in this paper, we improve some recent coupled fixed point resultsfor single-valued operators in the framework of ordered $b$-metricspaces established by bota et al. [m-f. bota, a. petrusel, g.petrusel and b. samet, coupled fixed point theorems forsingle-valued operators in b-metric spaces, fixed point theoryappl. (2015) 2015:231]. also, we prove that perov-type fixed pointtheorem in ordered gen...