scholarly journals Focal surfaces of hyperbolic cylinders

2017 ◽  
Author(s):  
Georgi Hristov Georgiev ◽  
Milen Dimov Pavlov
Keyword(s):  
Hyperbolic Cylinders

scholarly journals Hyperbolic cylinders and entanglement entropy: gravitons, higher spins, p-forms

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Justin R. David ◽  
Jyotirmoy Mukherjee
Keyword(s):  
Stress Tensor ◽  
Entanglement Entropy ◽  
Partition Functions ◽  
Point Function ◽  
Expectation Value ◽  
Massive Spin ◽  
Twist Operator ◽  
Higher Spins ◽  
Hyperbolic Cylinders ◽  
Kaluza Klein

Abstract We show that the entanglement entropy of D = 4 linearized gravitons across a sphere recently computed by Benedetti and Casini coincides with that obtained using the Kaluza-Klein tower of traceless transverse massive spin-2 fields on S1× AdS3. The mass of the constant mode on S1 saturates the Brietenholer-Freedman bound in AdS3. This condition also ensures that the entanglement entropy of higher spins determined from partition functions on the hyperbolic cylinder coincides with their recent conjecture. Starting from the action of the 2-form on S1× AdS5 and fixing gauge, we evaluate the entanglement entropy across a sphere as well as the dimensions of the corresponding twist operator. We demonstrate that the conformal dimensions of the corresponding twist operator agrees with that obtained using the expectation value of the stress tensor on the replica cone. For conformal p-forms in even dimensions it obeys the expected relations with the coefficients determining the 3-point function of the stress tensor of these fields.

scholarly journals New characterizations for hyperbolic cylinders in anti-de Sitter spaces

2012 ◽  
Vol 393 (1) ◽  
pp. 166-176 ◽  
Author(s):  
R.M.B. Chaves ◽  
L.A.M. Sousa ◽  
B.C. Valério
Keyword(s):  
De Sitter ◽  
Hyperbolic Cylinders

scholarly journals The Solution of Mathteu's Differential Equation

1915 ◽  
Vol 34 ◽  
pp. 176-196 ◽  
Author(s):  
John Dougall
Keyword(s):  
Differential Equation ◽  
Harmonic Functions ◽  
Hypergeometric Equation ◽  
Successful Theory ◽  
The One ◽  
Hyperbolic Cylinders ◽  
Degenerate Cases

The determination of the harmonic functions of elliptic and hyperbolic cylinders depends on the solution of Mathieu's differential equation. This equation, it has been remarked by Professor Whittaker, is the one which naturally comes up for study after the hypergeometric equation has been disposed of. Its solution presents difficulties which do not arise in connection with the hypergeometric equation or its degenerate cases, and it cannot, I think, be said that any discussion of the equation has yet been given with which the student of analysis can rest content. The treatment given below, though certainly incomplete at some points, seetns to follow the lines along which a thoroughly successful theory may be hoped for.

New characterizations of spacelike hyperplanes in the steady state space

2020 ◽  
Vol 126 (1) ◽  
pp. 61-72
Author(s):  
Cícero P. Aquino ◽  
Halyson I. Baltazar ◽  
Henrique F. De Lima
Keyword(s):  
Steady State ◽  
State Space ◽  
Riemannian Manifolds ◽  
De Sitter ◽  
Main Hypothesis ◽  
Spacelike Hypersurfaces ◽  
Open Region ◽  
Complete Riemannian Manifolds ◽  
Generalized Maximum Principle ◽  
Hyperbolic Cylinders

In this article, we deal with complete spacelike hypersurfaces immersed in an open region of the de Sitter space $\mathbb {S}^{n+1}_{1}$ which is known as the steady state space $\mathcal {H}^{n+1}$. Under suitable constraints on the behavior of the higher order mean curvatures of these hypersurfaces, we are able to prove that they must be spacelike hyperplanes of $\mathcal {H}^{n+1}$. Furthermore, through the analysis of the hyperbolic cylinders of $\mathcal {H}^{n+1}$, we discuss the importance of the main hypothesis in our results. Our approach is based on a generalized maximum principle at infinity for complete Riemannian manifolds.

scholarly journals Partition functions of higher derivative conformal fields on conformally related spaces

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Jyotirmoy Mukherjee
Keyword(s):  
Partition Function ◽  
Integral Representation ◽  
Gauge Field ◽  
Partition Functions ◽  
Conformal Vector ◽  
Higher Derivative ◽  
Conformal Fields ◽  
Vector Gauge ◽  
Bulk Part ◽  
Hyperbolic Cylinders

Abstract The character integral representation of one loop partition functions is useful to establish the relation between partition functions of conformal fields on Weyl equivalent spaces. The Euclidean space Sa × AdSb can be mapped to Sa+b provided Sa and AdSb are of the same radius. As an example, to begin with, we show that the partition function in the character integral representation of conformally coupled free scalars and fermions are identical on Sa × AdSb and Sa+b. We then demonstrate that the partition function of higher derivative conformal scalars and fermions are also the same on hyperbolic cylinders and branched spheres. The partition function of the four-derivative conformal vector gauge field on the branched sphere in d = 6 dimension can be expressed as an integral over ‘naive’ bulk and ‘naive’ edge characters. However, the partition function of the conformal vector gauge field on $$ {S}_q^1 $$ S q 1 × AdS5 contains only the ‘naive’ bulk part of the partition function. This follows the same pattern which was observed for the partition of conformal p-form fields on hyperbolic cylinders. We use the partition function of higher derivative conformal fields on hyperbolic cylinders to obtain a linear relationship between the Hofman-Maldacena variables which enables us to show that these theories are non-unitary.

Vibrations of Plates Bounded by Parts of Elliptical and Hyperbolic Cylinders

1966 ◽  
Vol 40 (6) ◽  
pp. 1534-1539 ◽  
Author(s):  
Ebenezer N. Krishnappa ◽  
W. R. Callahan
Keyword(s):  
Hyperbolic Cylinders

XVII.—Some Hyperspace Harmonic Analysis Problems introducing Extensions of Mathieu's Equation

1927 ◽  
Vol 46 ◽  
pp. 206-209 ◽  
Author(s):  
Pierre Humbert
Keyword(s):  
Harmonic Analysis ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Orthogonal System ◽  
Mathieu’S Equation ◽  
Image Position ◽  
Hyperbolic Cylinders ◽  
Three Dimensional Space

It is well known that two problems of harmonic analysis in ordinary three-dimensional space can be solved by Mathieu's functions, namely, (a) harmonic analysis for an orthogonal system of elliptic (or hyperbolic) cylinders,(b) harmonic analysis for a system of confocal paraboloïds,

scholarly journals Ellipsoidal functions and their application to some wave problems

1933 ◽  
Vol 232 (707-720) ◽  
pp. 223-283 ◽  
Keyword(s):  
Wave Motion ◽  
Circular Disc ◽  
Circular Aperture ◽  
Mathieu Functions ◽  
Physical Interest ◽  
Ellipsoid Of Revolution ◽  
Hypergeometric Type ◽  
Wave Problems ◽  
Hyperbolic Cylinders ◽  
Great Complexity

The analysis of wave motion connected with the circular disc and circular aperture is of such great analytical and physical interest, that no excuse is required for a somewhat extended treatment. The theory of wave motion has been very fully developed when the surfaces bounding the medium in which the motion takes place are spheres and circular cones, or cylinders and planes. The functions involved in the analysis are of the hypergeometric type. Next in order of importance is the theory required for the treatment of problems in which the surfaces bounding the medium are :— A. Ellipsoids of revolution and hyperboloids of revolution of one and two sheets ; B. Elliptic and hyperbolic cylinders. The functions involved in case A are functions associated with the ellipsoid of revolution, or spheroid. The functions involved in case B are commonly called MATHIEU functions. The MATHIEU functions and the functions associated with the ellipsoid of revolution are of considerable importance but, unfortunately, of great complexity.

scholarly journals New characterizations of hyperbolic cylinders in semi-Riemannian space forms

2016 ◽  
Vol 434 (1) ◽  
pp. 765-779
Author(s):  
Henrique F. de Lima ◽  
Fábio R. dos Santos ◽  
Marco Antonio L. Velásquez
Keyword(s):  
Riemannian Space ◽  
Space Forms ◽  
Riemannian Space Forms ◽  
Hyperbolic Cylinders
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