<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msup></mml:math>-vanishing results for conformally flat manifolds and submanifolds

Hao, Lin

doi:10.1016/j.geomphys.2013.06.005

Cited by 5 publications

(5 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…∇|ω| p 2 -F|ω| 2p . (22) Fix x ∈ M and choose μ ∈ C ∞ 0 (B x (1)). Multiplying ( 22) by μ 2 |ω| p(q-2) with q ≥ 2 and integrating by parts, we have…”

Section: Discussionmentioning

confidence: 99%

“…However, not all higher-dimensional manifolds have locally conformally flat structure, and giving classification of locally conformally flat manifolds is important as well as difficult. However, under various geometric conditions, there are substantial research results on the classification of conformally flat Riemannian manifolds (see [2,5,6,14,18,22,29] for details).…”

Section: Introductionmentioning

confidence: 99%

“…For L p harmonic 1-forms, Han et al [18] obtained some vanishing and finiteness theorems for L p p-harmonic 1-forms on a locally conformally flat Riemannian manifold with some assumptions. Analogously, there is substantial research indicating that the topologies of the submanifolds is closely associated with L p harmonic 1-forms; see [4,7,8,15,17,19,22] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

$L^{p}$ harmonic 1-forms on conformally flat Riemannian manifolds

Feng

Zhao

2021

J Inequal Appl

View full text Add to dashboard Cite

In this paper, we establish a finiteness theorem for $L^{p}$ L p harmonic 1-forms on a locally conformally flat Riemannian manifold under the assumptions on the Schrödinger operators involving the squared norm of the traceless Ricci form. This result can be regarded as a generalization of Han’s result on $L^{2}$ L 2 harmonic 1-forms.

show abstract

“…∇|ω| p 2 -F|ω| 2p . (22) Fix x ∈ M and choose μ ∈ C ∞ 0 (B x (1)). Multiplying ( 22) by μ 2 |ω| p(q-2) with q ≥ 2 and integrating by parts, we have…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

$L^{p}$ harmonic 1-forms on conformally flat Riemannian manifolds

Feng

Zhao

2021

J Inequal Appl

View full text Add to dashboard Cite

show abstract

“…But not every higher dimensional manifold admits a locally conformally flat structure, and it is di‰cult to give a good classification of locally conformally flat Riemannaian manifolds. However, by adding various geometric conditions, many authors have given some partial classification for locally conformally flat Riemannian manifolds (for examples, [2,4,5,7,11,12,13], etc. ).…”

Section: Introductionmentioning

confidence: 99%

$L^{p}$ $p$-harmonic 1-forms on locally conformally flat Riemannian manifolds

Han¹,

Zhang²,

Liang³

2017

Kodai Math. J.

View full text Add to dashboard Cite

In this paper, we obtain some vanishing and finiteness theorems for L p p-harmonic 1-forms on a locally conformally flat Riemmannian manifolds which satisfies an integral pinching condition on the traceless Ricci tensor, and for which the scalar curvature satisfies pinching curvature conditions or the first eigenvalue of the Laplace-Beltrami operator of M is bounded by a suitable constant. Recently, H. Z. Lin [11], investigated the L 2 harmonic 1-form on locally con-518 2010 Mathematics Subject Classification. 53C21; 53C25.

show abstract

“…However, by adding various geometric conditions, many authors have given some partial classification for LCF Riemannian manifolds (see, for example, [4,6,5,8,7,9,14,16,19], etc. It is well known that a conformally flat manifold is a higher dimensional generalization of a Riemannian surface.…”

Section: Introductionmentioning

confidence: 99%

On the structure of conformally flat Riemannian manifolds

Hao

2015

Nonlinear Analysis: Theory, Methods & Applications

View full text Add to dashboard Cite

Lp-vanishing results for conformally flat manifolds and submanifolds

Cited by 5 publications

References 26 publications

$L^{p}$ harmonic 1-forms on conformally flat Riemannian manifolds

$L^{p}$ harmonic 1-forms on conformally flat Riemannian manifolds

$L^{p}$ $p$-harmonic 1-forms on locally conformally flat Riemannian manifolds

On the structure of conformally flat Riemannian manifolds

Contact Info

Product

Resources

About