scholarly journals Locally extremal geodesic loops on a Riemannian manifold

2018 ◽  
Vol 146 (9) ◽  
pp. 4029-4033
Author(s):  
José Luis Flores
Keyword(s):  
Riemannian Manifold ◽  
Geodesic Loops

Geodesic loops and periodic geodesics on a Riemannian manifold diffeomorphic to S 3

2007 ◽  
Vol 257 (2) ◽  
pp. 427-437 ◽  
Author(s):  
Regina Rotman
Keyword(s):  
Riemannian Manifold ◽  
Geodesic Loops

scholarly journals On Conjugate Points and Geodesic Loops in a Complete Riemannian Manifold

2015 ◽  
Vol 26 (3) ◽  
pp. 2221-2230 ◽  
Author(s):  
Shicheng Xu
Keyword(s):  
Riemannian Manifold ◽  
Complete Riemannian Manifold ◽  
Conjugate Points ◽  
Geodesic Loops

Improved algorithm of preserving global and local properties based on Riemannian manifold learning

2011 ◽  
Vol 30 (12) ◽  
pp. 3301-3303
Author(s):  
Wei WANG ◽  
Du-yan BI ◽  
Lei XIONG
Keyword(s):  
Riemannian Manifold ◽  
Manifold Learning ◽  
Local Properties ◽  
Global And Local ◽  
Improved Algorithm

Golden Riemannian structures on the tangent bundle with g-natural metrics

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2543-2554
Author(s):  
E. Peyghan ◽  
F. Firuzi ◽  
U.C. De
Keyword(s):  
Riemannian Manifold ◽  
Tangent Bundle ◽  
Riemannian Metric

Starting from the g-natural Riemannian metric G on the tangent bundle TM of a Riemannian manifold (M,g), we construct a family of the Golden Riemannian structures ? on the tangent bundle (TM,G). Then we investigate the integrability of such Golden Riemannian structures on the tangent bundle TM and show that there is a direct correlation between the locally decomposable property of (TM,?,G) and the locally flatness of manifold (M,g).

Spacetime symmetries

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Riemannian Manifold ◽  
Conservation Laws ◽  
Vector Fields ◽  
Killing Vector ◽  
Geodesic Equation ◽  
Spacetime Symmetries ◽  
Tensor Fields ◽  
Killing Vector Fields ◽  
Covariant Derivatives ◽  
Killing Equation

This chapter introduces tensor fields, covariant derivatives and the geodesic equation on a (pseudo-) Riemannian manifold. It discusses how symmetries of a general space-time can be found from the Killing equation, and how the existence of Killing vector fields is connected to global conservation laws.

scholarly journals Short geodesic loops and $$L^p$$ norms of eigenfunctions on large genus random surfaces

2021 ◽  
Author(s):  
Clifford Gilmore ◽  
Etienne Le Masson ◽  
Tuomas Sahlsten ◽  
Joe Thomas
Keyword(s):  
Random Surfaces ◽  
Large Genus ◽  
Short Geodesic ◽  
Geodesic Loops

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.

scholarly journals Hearing the shape of a compact Riemannian manifold with a finite number of piecewise impedance boundary conditions

1997 ◽  
Vol 20 (2) ◽  
pp. 397-402 ◽  
Author(s):  
E. M. E. Zayed
Keyword(s):  
Riemannian Manifold ◽  
Boundary Conditions ◽  
Finite Number ◽  
Spectral Function ◽  
Compact Riemannian Manifold ◽  
Smooth Boundary ◽  
Beltrami Operator ◽  
Smooth Functions ◽  
Impedance Boundary ◽  
Impedance Boundary Conditions

The spectral functionΘ(t)=∑i=1∞exp(−tλj), where{λj}j=1∞are the eigenvalues of the negative Laplace-Beltrami operator−Δ, is studied for a compact Riemannian manifoldΩof dimension “k” with a smooth boundary∂Ω, where a finite number of piecewise impedance boundary conditions(∂∂ni+γi)u=0on the parts∂Ωi(i=1,…,m)of the boundary∂Ωcan be considered, such that∂Ω=∪i=1m∂Ωi, andγi(i=1,…,m)are assumed to be smooth functions which are not strictly positive.

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