An application of Yau’s maximum principle to conformally flat spaces

Goldberg, Samuel I.

doi:10.1090/s0002-9939-1980-0565352-8

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Mimkl1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

1982

2019

Publication Types

Select...

Article5

Relationship

Self Cite0

Independent5

Authors

Journals

Cited by 8 publications

(2 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The theorems and corollaries of this paper supplement our results from [1] and the results of other authors from [2, Theorem 16.9]; [13]; [28] and [30].…”

Section: Introductionsupporting

confidence: 81%

On higher-order Codazzi tensors on complete Riemannian manifolds

2019

View full text Add to dashboard Cite

We prove several Liouville-type non-existence theorems for higher order Codazzi tensors and classical Codazzi tensors on complete and compact Riemannian manifolds, in particular. These results will be obtained by using theorems of the connections between the geometry of a complete smooth manifold and the global behavior of its subharmonic functions. In conclusion, we show applications of this method for global geometry of a complete locally conformally flat Riemannian manifold with constant scalar curvature because its Ricci tensor is a Codazzi tensor and for global geometry of a complete hypersurface in a standard sphere because its second fundamental form is also a Codazzi tensor.

show abstract

“…The theorems and corollaries of this paper supplement our results from [1] and the results of other authors from [2, Theorem 16.9]; [13]; [28] and [30].…”

Section: Introductionsupporting

confidence: 81%

On higher-order Codazzi tensors on complete Riemannian manifolds

2019

View full text Add to dashboard Cite

show abstract

“…Remark. If on a conformally flat Riemannian manifold with positive constant scalar curvature R, trace Q2 = R2/(n -1) everywhere, then it follows easily [2,Theorem 3] that M is a Riemannian product of a space form Mx, with a 1-dimensional Riemannian manifold N, i.e., M = Mx X N.…”

Section: Mimklmentioning

confidence: 99%