On the geometry of Einstein-type structures

DOI10.1016/j.na.2020.112198OpenAlexW3109340914MaRDI QIDQ2227841

Giulio Colombo, Marco Rigoli, Andrea Anselli

Publication date: 16 February 2021

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2020.112198

zbMATH Keywords

weak maximum principleintegrability conditionsuniqueness resultswarped productsrigidity resultsnon-existence resultsvolume estimatesCodazzi tensorscurvature restrictions\( \varphi \)-curvaturesconformally harmonic-Einstein manifoldsharmonic-Einstein manifolds

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Rigidity results (53C24) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Local Riemannian geometry (53B20)

Related Items (6)

Gradient Einstein-type structures immersed into a Riemannian warped product ⋮ On the rigidity of harmonic-Ricci solitons ⋮ Einstein-type structures, Besse's conjecture, and a uniqueness result for a \(\varphi \)-CPE metric in its conformal class ⋮ Rigidity of compact almost Ricci solitons and applications of Pohozaev-Schoen identity ⋮ On a quadratic functional of the \(\varphi \)-scalar curvature ⋮ Bach and Einstein’s equations in presence of a field

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Generalized quasi-Einstein manifolds with harmonic Weyl tensor
• A note on Killing fields and CMC hypersurfaces
• On the \(h\)-almost Ricci soliton
• The Ricci-Bourguignon flow
• Rigidity of quasi-Einstein metrics
• The nonexistence of quasi-Einstein metrics
• Remarks on non-compact gradient Ricci solitons
• Yamabe-type equations on complete, noncompact manifolds
• Liouville type theorems for \(\varphi\)-subharmonic functions.
• ``A priori estimates, uniqueness and existence of positive solutions of Yamabe type equations on complete manifolds
• Spectral radius, index estimates for Schrödinger operators and geometric applications
• Keller-Osserman conditions for diffusion-type operators on Riemannian manifolds
• Ricci deformation of the metric on a Riemannian manifold
• Positive solutions of elliptic equations
• A Schwarz-type lemma for noncompact manifolds with boundary and geometric applications
• The maximum principle for hypersurfaces with vanishing curvature functions
• A note on curvature of Riemannian manifolds
• A compact gradient generalized quasi-Einstein metric with constant scalar curvature
• On Bach-flat gradient shrinking Ricci solitons
• On the geometry of \(\varphi\)-curvatures
• Compact almost Ricci solitons with constant scalar curvature are gradient
• On the geometry of gradient Einstein-type manifolds
• Obstructions to conformally Einstein metrics in \(n\) dimensions
• Vanishing theorems on Riemannian manifolds, and geometric applications
• Certain conditions for a Riemannian manifold to be isometric with a sphere
• On Ricci-harmonic metrics
• Ricci flow coupled with harmonic map flow
• Ricci almost solitons
• Maximum Principles and Geometric Applications
• On Representing Homotopy Classes by Harmonic Maps
• The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
• Hypersurfaces and a Pinching Problem on the Second Fundamental Tensor
• Rigidity of (m,ρ)-quasi Einstein manifolds
• Maximum principles on Riemannian manifolds and applications
• A remark on the maximum principle and stochastic completeness
• Compact Einstein warped product spaces with nonpositive scalar curvature
• On some aspects of oscillation theory and geometry

This page was built for publication: On the geometry of Einstein-type structures