Generalized tensor analysis in the sense of Colombeau’s construction is employed to introduce a nonlinear distributional pseudo-Riemannian geometry. In particular, after deriving several characterizations of invertibility in the algebra of generalized functions we define the notions of generalized pseudo-Riemannian metric, generalized connection and generalized curvature tensor. We prove a “Fun...

Citation Hohm, Olaf, and Barton Zwiebach. "Double metric, generalized metric, and-deformed double field theory. Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. We ...

In this paper we present inequalities between two generalizations of the hyperbolic metric and the jG metric. We also prove inequalities between generalized versions of the jG metric and Seittenranta’s metric.

Very recently, Lin et al. [1] introduced the notion of generalized quasi-metric inspired from the notion of generalized metric, defined by Branciari [2]. It is a very well-known fact that the concept of generalizedmetric can be derived from the definition ofmetric by replacing the triangle inequality with a weaker condition, namely, quadrilateral inequality. In spite of the analogy between the ...

In this paper the metric dimension of (the incidence graphs of) particular partial linear spaces is considered. We prove that the metric dimension of an affine plane of order q ≥ 13 is 3q − 4 and describe all resolving sets of that size if q ≥ 23. The metric dimension of a biaffine plane (also called a flag-type elliptic semiplane) of order q ≥ 4 is shown to fall between 2q−2 and 3q−6, while fo...

The work investigates the powerlocales (lower, upper, Vietoris) of localic completions of generalized metric spaces. The main result is that all three are localic completions of generalized metric powerspaces, on the Kuratowski finite powerset. Applications: (1) A localic completion is always open, and is compact iff its generalized metric space is totally bounded. (2) The Heine-Borel Theorem i...

Let C(X) be the hyperspace of all subcontinua of a metric continuum X. Alejandro Illanes has proved that C(X) is a finitedimensional Cartesian product if and only if X is an arc or a circle. In this paper we shall prove, using the inverse systems and limits, that if X is a non-metric rim-metrizable continuum and C(X) is a finitedimensional Cartesian product, then X is a generalized arc or a gen...

Correspondence: [email protected] Graduate School of Science and Engineering, Yamaguchi University, 755-8611 Une, Japan Full list of author information is available at the end of the article Abstract In this paper, we give a Heisenberg type or a Schrödinger-type uncertainty relation for generalized metric adjusted skew information or generalized metric adjusted correlation measure. These...

We present sufficient conditions for the existence of solutions of second-order two-point boundary value and fractional order functional differential equation problems in a space where self distance is not necessarily zero. For this, first we introduce a Ciric type generalized F-contraction and F- Suzuki contraction in a metric-like space and give relevance to fixed point results. To illustrate...