Homology groups in warped product submanifolds in hyperbolic spaces
type: Item
instance of: scholarly article
title: Homology groups in warped product submanifolds in hyperbolic spaces
zbMATH Open document ID: 1477.53086
DOI: 10.1155/2021/8554738
author: Yanlin Li
author: Akram Ali
author: Nadia Alluhaibi
author: Fatemah Y. Y. Mofarreh
published in: Journal of Mathematics
publication date: 2021-11-25T00:00:00Z
review text: Summary: In this paper, we show that if the Laplacian and gradient of the warping function of a compact warped product submanifold \(\Omega^{p + q}\) in the hyperbolic space \(\mathbb{H}^m(-1)\) satisfy various extrinsic restrictions, then \(\Omega^{p + q}\) has no stable integral currents, and its homology groups are trivial. Also, we prove that the fundamental group \(\pi_1(\Omega^{p + q})\) is trivial. The restrictions are also extended to the eigenvalues of the warped function, the integral Ricci curvature, and the Hessian tensor. The results obtained in the present paper can be considered as generalizations of the Fu-Xu theorem in the framework of the compact warped product submanifold which has the minimal base manifold in the corresponding ambient manifolds.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 7433570
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/8554738
OpenAlex ID: W3202302296
Wikidata QID: Q115521406
cites work: Normal and integral currents
cites work: On stable currents and their application to global problems in real and complex geometry
cites work: VANISHING AND TOPOLOGICAL SPHERE THEOREMS FOR SUBMANIFOLDS IN A HYPERBOLIC SPACE
cites work: Biharmonic submanifolds of Kaehler product manifolds
cites work: A general inequality for CR-warped products in generalized Sasakian space form and its applications
cites work: Tangent developables and Darboux developables of framed curves
cites work: Lightlike tangent developables in de Sitter 3-space
cites work: Geometric algebra of singular ruled surfaces
cites work: Slant helix of order n and sequence of Darboux developables of principal‐directional curves
cites work: Ricci curvature for warped product submanifolds of Sasakian space forms and its applications to differential equations
cites work: Topological and differentiable sphere theorems for complete submanifolds
cites work: Differentiable sphere theorems for submanifolds of positive \(k\)-th Ricci curvature
cites work: Geometric, topological and differentiable rigidity of submanifolds in space forms
cites work: Nonexistence of stable currents in submanifolds of a product of two spheres
cites work: The RICCI curvature of submanifolds and its applications
cites work: Homology vanishing theorems for submanifolds
cites work: Stable currents and homology groups in a compact CR-warped product submanifold with negative constant sectional curvature
cites work: Null homology in warped product Lagrangian submanifolds of the nearly Kaehler \(\mathbb{S}^6\) and its applications
cites work: Mean curvature flow of pinched submanifolds to spheres
cites work: Q4345356
cites work: Manifolds of Negative Curvature
cites work: Q3312869
cites work: ON ISOMETRIC MINIMAL IMMERSIONS FROM WARPED PRODUCTS INTO REAL SPACE FORMS
cites work: Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
description: scientific article; zbMATH DE number 7433570