The topological structure of conformally flat Riemannian manifolds
type: Item
instance of: scholarly article
title: The topological structure of conformally flat Riemannian manifolds
zbMATH Open document ID: 1395.53041
published in: Results in Mathematics
publication date: 2018-07-23T00:00:00Z
review text: The paper investigates the influence of the index of a Schrödinger operator defined on a locally conformal manifold upon some topological and geometric properties of the manifold.
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 6909673
zbMATH Keywords: harmonic 1-form
zbMATH Keywords: finite index
zbMATH Keywords: nonparabolic end
author: Yingbo Han
reviewed by: Dumitru Motreanu
MaRDI profile type: Publication
full work available at URL: s00025-018-0812-y
OpenAlex ID: W2791348481
Wikidata QID: Q115389851
cites work: Q4424457
cites work: The Huber theorem for non-compact conformally flat manifolds
cites work: \(L^2\)-harmonic 1-forms on submanifolds with finite total curvature
cites work: A gap theorem for complete noncompact manifolds with nonnegative Ricci curvature
cites work: COMPACT LOCALLY CONFORMALLY FLAT RIEMANNIAN MANIFOLDS
cites work: Total curvature and \(L ^{2}\) harmonic 1-forms on complete submanifolds in space forms
cites work: An Application of Yau's Maximum Principle to Conformally Flat Spaces
cites work: Conformally Flat Manifolds and a Pinching Problem on the Ricci Tensor
cites work: The topological structure of complete noncompact submanifolds in spheres
cites work: \(L^{p}\) \(p\)-harmonic 1-forms on locally conformally flat Riemannian manifolds
cites work: On the Sobolev constant and the $p$-spectrum of a compact riemannian manifold
cites work: Harmonic functions and the structure of complete manifolds
cites work: Minimal hypersurfaces with finite index
cites work: \(L^p\)-vanishing results for conformally flat manifolds and submanifolds
cites work: On the structure of conformally flat Riemannian manifolds
cites work: \(L^2\) harmonic forms on submanifolds in a Hadamard manifold
cites work: The geometric properties of harmonic function on 2-dimensional Riemannian manifolds
cites work: \(L^p\) Ricci curvature pinching theorems for conformally flat Riemannian manifolds
cites work: A gap theorem on submanifolds with finite total curvature in spheres
cites work: Finiteness of non-parabolic ends on submanifolds in spheres
DOI: 10.1007/S00025-018-0812-Y
description: scientific article; zbMATH DE number 6909673