On the Minimal Eigenvalue of the Laplacian Operator for p-Forms in Conformally Flat Riemannian Manifolds

1982 ◽  
Vol 86 (1) ◽  
pp. 103 ◽  
Author(s):  
Domenico Perrone
Keyword(s):  
Riemannian Manifolds ◽  
Laplacian Operator ◽  
Conformally Flat ◽  
Minimal Eigenvalue

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

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jing Li ◽  
Shuxiang Feng ◽  
Peibiao Zhao
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Finiteness Theorem ◽  
Conformally Flat ◽  
Locally Conformally Flat ◽  
Flat Riemannian Manifold ◽  
Ricci Form

AbstractIn 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.

Geometries and Topologies of Conformally Flat Riemannian Manifolds

2020 ◽  
Vol 46 (6) ◽  
pp. 1683-1695
Author(s):  
Jing Li ◽  
Shuxiang Feng ◽  
Peibiao Zhao
Keyword(s):  
Riemannian Manifolds ◽  
Conformally Flat

scholarly journals Harmonic morphisms with one-dimensional fibres on conformally-flat Riemannian manifolds

2008 ◽  
Vol 145 (1) ◽  
pp. 141-151 ◽  
Author(s):  
RADU PANTILIE
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Harmonic Morphisms ◽  
Two Dimensional ◽  
Conformally Flat ◽  
Harmonic Morphism ◽  
One Dimensional ◽  
Dimension 2 ◽  
Real Analytic ◽  
Flat Riemannian Manifold

AbstractWe classify the harmonic morphisms with one-dimensional fibres (1) from real-analytic conformally-flat Riemannian manifolds of dimension at least four (Theorem 3.1), and (2) between conformally-flat Riemannian manifolds of dimensions at least three (Corollaries 3.4 and 3.6).Also, we prove (Proposition 2.5) an integrability result for any real-analytic submersion, from a constant curvature Riemannian manifold of dimensionn+2 to a Riemannian manifold of dimension 2, which can be factorised as ann-harmonic morphism with two-dimensional fibres, to a conformally-flat Riemannian manifold, followed by a horizontally conformal submersion, (n≥4).

Eigenvalues of the Laplacian Operator and Neighborhood Enlargement for Compact Manifolds

2020 ◽  
pp. 84-102
Keyword(s):  
Laplace Operator ◽  
Riemannian Manifolds ◽  
Compact Manifolds ◽  
Laplacian Operator ◽  
Measure Concentration ◽  
Eigenvalues Of The Laplacian ◽  
The Laplace Operator ◽  
Concentration Phenomenon

In this investigation and under the conception of measure concentration phenomenon we found that the enlargement of the neighborhood for an n – dimensional compact Riemannian manifolds (M,g) relative to the eigenvalues λ of the Laplace operator ∆ on (M,g). And we found that r~1/√λ. تناول هذا البحث تجسيم الجوار لمتعدد الطيات المتراص في البعد n وذلك باستخدام مفهوم تركيز الحجم. كما وجدنا أن نصف القطر r لتجسيم الجوار لمتعدد الطيات يرتبط مع القيم الذاتية λ لمؤثر لابلاس Δ على متعدد الطيات. الكلمات المفتاحية: نصف قطر تجسيم الجوار، متباينات متساوي المقاييس، تركيز الحجم، مؤثر لابلاس، القيم الذاتية لمؤثر لابلاس.

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