A Characterization of Ruled Real Hypersurfaces in Non-Flat Complex Space Forms

The Levi-Civita connection and the k-th generalized Tanaka-Webster connection are defined on a real hypersurface M in a non-flat complex space form. For any nonnull constant k and any vector field X tangent to M the k-th Cho operator F X ( k ) is defined and is related to both connections. If X belongs to the maximal holomorphic distribution D on M, the corresponding operator does not depend on k and is denoted by F X and called Cho operator. In this paper, real hypersurfaces in non-flat space forms such that F X S = S F X , where S denotes the Ricci tensor of M and a further condition is satisfied, are classified

Geometry of Submanifolds and Homogeneous Spaces

The present Special Issue of Symmetry is devoted to two important areas of global Riemannian geometry, namely submanifold theory and the geometry of Lie groups and homogeneous spaces. Submanifold theory originated from the classical geometry of curves and surfaces. Homogeneous spaces are manifolds that admit a transitive Lie group action, historically related to F. Klein's Erlangen Program and S. Lie's idea to use continuous symmetries in studying differential equations. In this Special Issue, we provide a collection of papers that not only reflect some of the latest advancements in both areas, but also highlight relations between them and the use of common techniques. Applications to other areas of mathematics are also considered

On a New type of Tensor on Real Hypersurfaces in Non-Flat Complex Space Forms

In this paper the notion of ∗ -Weyl curvature tensor on real hypersurfaces in non-flat complex space forms is introduced. It is related to the ∗ -Ricci tensor of a real hypersurface. The aim of this paper is to provide two classification theorems concerning real hypersurfaces in non-flat complex space forms in terms of ∗ -Weyl curvature tensor. More precisely, Hopf hypersurfaces of dimension greater or equal to three in non-flat complex space forms with vanishing ∗ -Weyl curvature tensor are classified. Next, all three dimensional real hypersurfaces in non-flat complex space forms, whose ∗ -Weyl curvature tensor vanishes identically are classified. The used methods are based on tools from differential geometry and solving systems of differential equations

Das Einheiten-Umverteilungs-Problem

We describe the problem of re-balancing a number of units distributed over a geographic area. Each unit consists of a number of components. A value between 0 and 1 describes the current rating of each component. By a piecewise linear function this value is converted into a nominal status assessment. The lowest of the statuses determines the efficiency of a unit, and the highest status its cost. An unbalanced unit has a gap between these two. To re-balance the units, components can be transferred. The goal is to maximize the efficiency of all units. On a secondary level, the cost for the re-balancing should be minimal. We present a mixed-integer nonlinear programming formulation for this problem, which describes the potential movement of components as a multi-commodity flow. The piecewise linear functions needed to obtain the status values are reformulated using inequalities and binary variables. This results in a mixed-integer linear program, and numerical standard solvers are able to compute proven optimal solutions for instances with up to 100 units. We present numerical solutions for a set of test instances and a bi-criteria objective function, and discuss the trade-off between cost and efficiency.Wir beschreiben das Problem der Umverteilung einer Anzahl von Einheiten, die über ein geografisches Gebiet verteilt sind. Jede Einheit besteht aus einer Reihe von Komponenten. Ein Wert zwischen 0 und 1 beschreibt die aktuelle Bewertung jeder Komponente. Durch eine stückweise lineare Funktion wird dieser Wert in eine nominale Zustandsbewertung umgerechnet. Der niedrigste Status bestimmt die Effizienz einer Einheit und der höchste Status seine Kosten. Eine unausgeglichene Einheit weist eine Lücke zwischen diesen beiden auf. Um die Einheiten neu auszubalancieren, können Komponenten übertragen werden. Ziel ist es, die Effizienz aller Einheiten zu maximieren. Auf einer untergeordneten Ebene sollten die Kosten für die Umverteilung minimal sein. Für dieses Problem stellen wir eine gemischt-ganzzahlige nichtlineare Modellformulierung vor, die die potenzielle Bewegung von Komponenten als Mehrgüterfluss beschreibt. Die stückweise linearen Funktionen, die zum Erhalten der Statuswerte benötigt werden, werden unter Verwendung von Ungleichungen und binären Variablen umformuliert. Dies führt zu einem gemischt-ganzzahligen linearen Programm, und numerische Standardlöser sind in der Lage, beweisbar optimale Lösungen für Instanzen mit bis zu 100 Einheiten zu berechnen. Wir präsentieren numerische Lösungen für eine Reihe von Testinstanzen und eine bikriterielle Zielfunktion und diskutieren den Kompromiss zwischen Kosten und Effizienz

Hedging effectiveness for international index futures markets

This paper investigates the hedging effectiveness of the International Index Futures Markets using daily settlement prices for the period 4 January 2010 to 31 December 2015. Standard OLS regressions, Error Correction Model (ECM), as well as Autoregressive Distributed Lag (ARDL) cointegration model are employed to estimate corresponding hedge ratios that can be employed in risk management. The analyzed sample consists of daily closing market rates of the stock market indexes of the USA and the European futures contracts. The findings indicate that the time varying hedge ratios, if estimated through the ARDL model, are more efficient than the fixed hedge ratios in terms of minimizing the risk. Additionally, there is evidence that the comparative advantage of advanced econometric approaches compared to conventional models is enhanced further for capital markets within peripheral EU countrie

Helicoidal hypersurfaces in the four dimensional minkowski space

Helicoidal hypersurfaces in the four dimensional Minkowski space are defined. There are three types, depending on the axis of rotation. Equations for the Gaussian and mean curvature are derived and many examples of the various types of hypersurfaces are given. A theorem classifying the helicoids with timelike axes and ΔH=AH is obtained

A Characterization of Ruled Real Hypersurfaces in Non-Flat Complex Space Forms

The authors would like to thank the reviewers for their valuable comments in order to improve the paper.The Levi-Civita connection and the k-th generalized Tanaka-Webster connection are defined on a real hypersurface M in a non-flat complex space form. For any nonnull constant k and any vector field X tangent to M the k-th Cho operator F (k) X is defined and is related to both connections. If X belongs to the maximal holomorphic distribution D on M, the corresponding operator does not depend on k and is denoted by FX and called Cho operator. In this paper, real hypersurfaces in non-flat space forms such that FXS = SFX, where S denotes the Ricci tensor of M and a further condition is satisfied, are classified