Related papers: A sectional curvature for statistical structures
We establish a new algebraic characterization of sectional curvature bounds $\sec\geq k$ and $\sec\leq k$ using only curvature terms in the Weitzenb\"ock formulae for symmetric $p$-tensors. By introducing a symmetric analogue of the…
The present text is a collection of notes about differential geometry prepared to some extent as part of tutorials about topics and applications related to tensor calculus. They can be regarded as continuation to the previous notes on…
In this paper, we study the computation of curvatures at the singular points of algebraic curves and surfaces. The idea is to convert the problem to compute the curvatures of the corresponding regular parametric curves and surfaces, which…
The divergences coming from a particular sector of gravitational fluctuations around a generic background in general theories of quadratic gravity are analyzed. They can be summarized in a particular type of scalar model, whose properties…
Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…
A general model for geometric structures on differentiable manifolds is obtained by deforming infinitesimal symmetries. Specifically, this model consists of a Lie algebroid, equipped with an affine connection compatible with the Lie…
A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.
This paper surveys some selected topics in the theory of conformal metrics and their connections to complex analysis, partial differential equations and conformal differential geometry.
In this article, we introduce the sectional curvature in contravariant warped product space $(M= M_{1}\times_{f_{1}}M_{2},\Pi,g^{f_{1}})$, where $\Pi=\Pi_1+\nu_{1}\Pi_2$). After that we find the sectional curvature of $M$ for which $M_{1}$…
We explore the notion of sectional number of a group homomorphism, leading to a generalization of the covering number of a group, and present several characterizations when the sectional number is finite, providing estimates for computing…
In this paper we have introduced a new symmetry property of spacetime which is named as semiconformal curvature collineation, and its relationship with other known symmetry properties has been established. This new symmetry property of the…
Based on two classical notions of curvature for curves in general metric spaces, namely the Menger and Haantjes curvatures, we introduce new definitions of sectional, Ricci and scalar curvature for networks and their higher dimensional…
In this paper, we give a new generalization of positive sectional curvature called positive weighted sectional curvature. It depends on a choice of Riemannian metric and a smooth vector field. We give several simple examples of Riemannian…
A brief survey of real algebraic structures on topological spaces is given. This article is written for the Gokova Gemetry/Topology Conference proceedings.
Key to structured prediction is exploiting the problem structure to simplify the learning process. A major challenge arises when data exhibit a local structure (e.g., are made by "parts") that can be leveraged to better approximate the…
In the geometric approach to define complexity, operator complexity is defined as the distance on the operator space. In this paper, based on the analogy with the circuit complexity, the operator size is adopted as the metric of the…
This is a short essay about some fundamental results on scalar curvature and the two key methods that are used to establish them.
In this paper, we give a simple formula for sectional curvatures on the general linear group, which is also valid for many other matrix groups. Similar formula is given for a reductive Lie group. We also discuss the relation between…
We have built a new kind of manifolds which leads to an alternative new geometrical space. The study of the nowhere differentiable functions via a family of mean functions leads to a new characterization of this category of functions. A…
In the article, we exhibit a series of new examples of rigid plane curves, that is, curves, whose collection of singularities determines them almost uniquely up to a projective transformation of the plane.