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TWO REMARKS ON THE LENGTH SPECTRUM OF A RIEMANNIAN MANIFOLD

by Benjamin Schmidt, Craig, J. Sutton
"... (Communicated by Jianguo Cao) Abstract. We demonstrate that every closed manifold of dimension at least two admits smooth metrics with respect to which the length spectrum is not a discrete subset of the real line. In contrast, we show that the length spectrum of any real analytic metric on a closed ..."
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closed manifold is a discrete subset of the real line. In particular, the length spectrum of any closed locally homogeneous space forms a discrete set. 1.

Boundary volume and length spectra of Riemannian manifolds: what the middle degree Hodge spectrum doesn’t reveal

by Carolyn S. Gordon, Juan, Pablo Rossetti - Ann. Inst. Fourier (Grenoble
"... Abstract. Let M be a 2m-dimensional compact Riemannian manifold. We show that the spectrum of the Hodge Laplacian acting on m-forms does not determine whether the manifold has boundary, nor does it determine the lengths of the closed geodesics. Among the many examples are a projective space and a he ..."
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Abstract. Let M be a 2m-dimensional compact Riemannian manifold. We show that the spectrum of the Hodge Laplacian acting on m-forms does not determine whether the manifold has boundary, nor does it determine the lengths of the closed geodesics. Among the many examples are a projective space and a

Foliation on the Moduli Space of Helices on a Real Space Form

by Toshiaki Adachi
"... In this note we study a foliation on the moduli space of helices of order not greater than 4 on a real space form which corresponds to length spectrum. ..."
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In this note we study a foliation on the moduli space of helices of order not greater than 4 on a real space form which corresponds to length spectrum.

the quantized space.

by Roman G. Vorobyov , 2008
"... It is shown, that the space quantum existence ( SQE) non-ambiguously determines the metrical form for the space without a time, using weak condition of metrical additivity. The hypothesis is proposed, Riemann metric is only possible for quantized space classes. This statement probably can close the ..."
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( see, for example [2] ) and there is not guaranty, that space metrical form is unique. The following approach probably closes the metrical form problem. Certainly, all spectrum of this problem is not discussed in this article, particularly, in cases, when global constants can be changed, etc

Quantisation on general spaces

by Ajay Patwardhan , 2002
"... Quantisation on spaces with properties of curvature, multiple connectedness and non orientablility is obtained. The geodesic length spectrum for the Laplacian operator is extended to solve the Schroedinger operator. Homotopy fundamental group representations are used to obtain a direct sum of Hilber ..."
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Quantisation on spaces with properties of curvature, multiple connectedness and non orientablility is obtained. The geodesic length spectrum for the Laplacian operator is extended to solve the Schroedinger operator. Homotopy fundamental group representations are used to obtain a direct sum

Extrinsic Symmetric Spaces

by Inkang Kim - Dissertation, Augsburg 2005, Shaker Verlag
"... Abstract. In this note we survey rigidity results in symmetric spaces. More precisely, if X and Y are symmetric spaces of noncompact type without Eu-clidean de Rham factor, with G1 and G2 corresponding semisimple Lie groups, and Γ1 ⊂ G1,Γ2 ⊂ G2 are Zariski dense subgroups with the same marked length ..."
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length spectrum, then X = Y and Γ1,Γ2 are conjugate by an isometry. As an application, we answer in the affirmative a Margulis’s question and show that the cross-ratio on the limit set determines the Zariski dense subgroups up to conjugacy. We also embeds the space of nonparabolic representations from Γ

ON TWO DISTANCES ON TEICHMÜLLER SPACE

by Hiroshige Shiga , 2003
"... We consider adistance $d_{L} $ on the Teichmüuller space $T(S_{0}) $ of a hyperbolic Riemann surface $S_{0} $. The distance is definffi by the length spectrum of Riemann suffacae in $T(S_{0})\mathrm{m}\mathrm{d} $ we $\mathrm{c}\mathrm{a}\mathrm{l} $ it the lengh $\mathrm{s}\mathrm{p}\mathrm{e}\math ..."
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We consider adistance $d_{L} $ on the Teichmüuller space $T(S_{0}) $ of a hyperbolic Riemann surface $S_{0} $. The distance is definffi by the length spectrum of Riemann suffacae in $T(S_{0})\mathrm{m}\mathrm{d} $ we $\mathrm{c}\mathrm{a}\mathrm{l} $ it the lengh $\mathrm

Fractal Quantum Space-Time

by Leonardo Modesto , 905
"... In this paper we calculated the spectral dimension of loop quantum gravity (LQG) using the scaling property of the area operator spectrum on spin-network states and using the scaling property of the volume and length operators on Gaussian states. We obtained that the spectral dimension of the spatia ..."
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In this paper we calculated the spectral dimension of loop quantum gravity (LQG) using the scaling property of the area operator spectrum on spin-network states and using the scaling property of the volume and length operators on Gaussian states. We obtained that the spectral dimension

On the rigidity of discrete isometry groups of negatively curved spaces

by Sa’ar Hersonsky , Frédéric Paulin - COMMENTARII MATHEMATICI HELVETICI , 1997
"... We prove an ergodic rigidity theorem for discrete isometry groups of CAT(−1) spaces. We give explicit examples of divergence isometry groups with infinite covolume in the case of trees, piecewise hyperbolic 2-polyhedra, hyperbolic Bruhat-Tits buildings and rank one symmetric spaces. We prove that t ..."
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Riemannian metric, with conical singularities of angles at least 2π, on a closed surface, is determined, up to isometry, by its marked length spectrum.

Cassini imaging science: Instrument characteristics and anticipated scientific investigations at Saturn. Space Sci

by Carolyn C. Porco, Robert A. West, Steven Squyres, Peter Thomas, Carl D. Murray, Anthony Delgenio, Andrew P. Ingersoll, Torrence V. Johnson, Gerhard Neukum, Joseph Veverka, Luke Dones, Andre Brahic, Joseph A. Burns, Vance Haemmerle Benjamin Knowles, Thomas Roatsch, Kevin Beurle, William Owen - Rev , 2004
"... Abstract. The Cassini Imaging Science Subsystem (ISS) is the highest-resolution two-dimensional imaging device on the Cassini Orbiter and has been designed for investigations of the bodies and phenomena found within the Saturnian planetary system. It consists of two framing cameras: a narrow angle, ..."
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, reflecting telescope with a 2-m focal length and a square field of view (FOV) 0.35 ◦ across, and a wide-angle refractor with a 0.2-m focal length and a FOV 3.5 ◦ across. At the heart of each camera is a charged coupled device (CCD) detector consisting of a 1024 square array of pixels, each 12 µ on a side
Results 11 - 20 of 449