Haller, Stefan Vizman, Cornelia
Published in
Annals of Global Analysis and Geometry

A nonlinear flag is a finite sequence of nested closed submanifolds. We study the geometry of Fréchet manifolds of nonlinear flags, in this way generalizing the nonlinear Grassmannians. As an application, we describe a class of coadjoint orbits of the group of Hamiltonian diffeomorphisms that consist of nested symplectic submanifolds, i.e., symplec...

Maeta, Shun
Published in
Annals of Global Analysis and Geometry

In this paper, we classify three-dimensional complete gradient Yamabe solitons with divergence-free Cotton tensor. We also give some classifications of complete gradient Yamabe solitons with nonpositively curved Ricci curvature in the direction of the gradient of the potential function.

Grant, James D. E. Kunzinger, Michael Sämann, Clemens
Published in
Annals of Global Analysis and Geometry

We study the low-regularity (in-)extendibility of spacetimes within the synthetic-geometric framework of Lorentzian length spaces developed in Kunzinger and Sämann (Ann Glob Anal Geom 54(3):399–447, 2018). To this end, we introduce appropriate notions of geodesics and timelike geodesic completeness and prove a general inextendibility result. Our re...

Moroianu, Andrei Nagy, Paul-Andi
Published in
Annals of Global Analysis and Geometry

We show that 6-dimensional strict nearly Kähler manifolds admitting effective T3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {T}}^3$$\end{document} actions ...

Shouman, Abdolhakim
Published in
Annals of Global Analysis and Geometry

In the present paper, we first consider the weighted eigenvalue problem Δfu=λfu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta _f u=\lambda _{f}u$$\end{document}...

Suárez-Serrato, P. Torres Orozco, J. Vera, R.
Published in
Annals of Global Analysis and Geometry

We show that generalized broken fibrations in arbitrary dimensions admit rank-2 Poisson structures compatible with the fibration structure. After extending the notion of wrinkled fibration to dimension 6, we prove that these wrinkled fibrations also admit compatible rank-2 Poisson structures. In the cases with indefinite singularities, we can provi...

Carriazo, Alfonso Martín-Molina, Verónica Vrancken, Luc
Published in
Annals of Global Analysis and Geometry

We present classifications of totally geodesic and totally umbilical Legendrian submanifolds of (κ,μ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\kappa ,\mu )$$\en...

Amiri, Habib Schmeding, Alexander
Published in
Annals of Global Analysis and Geometry

The present paper links the representation theory of Lie groupoids and infinite-dimensional Lie groups. We show that smooth representations of Lie groupoids give rise to smooth representations of associated Lie groups. The groups envisaged here are the bisection group and a group of groupoid self-maps. Then, representations of the Lie groupoids giv...

Catino, Giovanni Mastrolia, Paolo
Published in
Annals of Global Analysis and Geometry

The aim of this paper is to study new classes of Riemannian manifolds endowed with a smooth potential function, including in a general framework classical canonical structures such as Einstein, harmonic curvature and Yamabe metrics, and, above all, gradient Ricci solitons. For the most rigid cases, we give a complete classification, while for the o...

Opozda, Barbara
Published in
Annals of Global Analysis and Geometry

In the paper two important theorems about complete affine spheres are generalized to the case of statistical structures on abstract manifolds. The assumption about constant sectional curvature is replaced by the assumption that the curvature satisfies some inequalities.