/pdf/a-mapping-of-riemannian-manifolds-which-preserves-harmonic-woa2molyuf.pdf

A mapping of Riemannian manifolds which preserves harmonic functions

Expressions are derived for the free energy of a massless scalar gas confined to a spatial cavity in a static space-time at a finite temperature. A high temperature expansion is presented in terms of the Minakshisundaram coefficients. This gives curvature and boundary corrections to the Planckian form. The regularisation used is the zeta function one, and yields a finite total internal energy. However, it is known that the local energy density diverges in a non-integrable way as the boundary is approached. A 'surface energy' is suggested to reconcile these two facts. Explicit expressions for the total energy inside two infinite rectangular waveguides are obtained.

http://iopscience.iop.org/article/10.1088/0305-4470/11/5/020/pdf

Finite temperature and boundary effects in static space-times

Finite temperature field theory with boundaries: Stress tensor and surface action renormalisation

We compute the conformal anomaly in the free d = 6 superconformal (2,0) tensor multiplet theory on generic curved background. Up to a trivial covariant total-derivative term, it is given by the sum of the type A part proportional to the 6-d Euler density, and the type B part containing three independent conformal invariants. Multiplied by the factor 4N3, the latter Weyl-invariant part of the anomaly reproduces exactly the corresponding part of the conformal anomaly of large N multiple M5-brane (2,0) theory as predicted (hep-th/9806087) by AdS7 supergravity on the basis of AdS/CFT correspondence. The coefficients of the type A anomaly differ by the factor (4/7) × 4N3, so that the free tensor multiplet anomaly does not vanish on a Ricci-flat background. The coefficient 4N3 is the same as found (hep-th/9703040) in the comparison of the tensor multiplet theory and the d = 11 supergravity predictions for the absorption cross-sections of gravitons by M5 branes, and in the comparison (hep-th/9911135) of 2- and 3-point stress tensor correlators of the free tensor multiplet with the AdS7 supergravity predictions.

http://cds.cern.ch/record/420553/files/0001041.pdf

Conformal anomaly of (2,0) tensor multiplet in six-dimensions and AdS / CFT correspondence

(Here o~-~the volume of the unit ball in R\". The simplest expression for eo is w = (1]( 89 \"/~ where ({rn)! ---F( 89 + 1).) First we make several remarks. 1. Our method for attacking the conjecture (I) will be to use the power series expansion for Vm(r). This expansion will be considered in detail in section 3; however, the general facts about it are the following: (a) the first term in the series is corn; (b) the coefficient of r n+~ vanishes provided k is odd; (c) the coefficients of r n+~ for/r even can be expressed in terms of curvature. Unfortunately the nonzero coefficients depend on curvature in a rather complicated way, and this is what makes the resolution of the conjecture (I) an interesting problem. 2. To our knowledge the power series expansion for Vm(r) was first considered in 1848 by Bertrand-Diguet-Puiseux [6]. See also [14, p. 209]. In these papers the first two terms of the expansion for Fro(r) are computed for surfaces in RS:

/pdf/riemannian-geometry-as-determined-by-the-volumes-of-small-3rdzqoybnf.pdf

Riemannian geometry as determined by the volumes of small geodesic balls

/pdf/on-eigen-values-of-laplacian-and-curvature-of-riemannian-ien0wuy03b.pdf

On eigen-values of Laplacian and curvature of Riemannian manifold

https://projecteuclid.org/download/pdf_1/euclid.tmj/1178242590

On closed geodesics of lens spaces

/pdf/three-remarks-on-fundamental-groups-of-some-riemannian-qes4jnwcrw.pdf

Three remarks on fundamental groups of some Riemannian manifolds

/pdf/on-pu-s-theorem-for-odd-dimensional-real-projective-spaces-27e1bkipqe.pdf

On pu's theorem for odd dimensional real projective spaces

/pdf/the-contact-structures-on-su-n-1-r-su-n-r-a-and-sp-n-su-2-sp-4gogwc0i22.pdf

Takashi Sakai

Papers

On eigen-values of Laplacian and curvature of Riemannian manifold

On closed geodesics of lens spaces

Three remarks on fundamental groups of some Riemannian manifolds

On pu's theorem for odd dimensional real projective spaces

THE CONTACT STRUCTURES ON {{ SU(n + 1) × R/SU(n) × R} _α } AND {{ Sp(n) × SU(2)/Sp(n - 1) × SU(2)} _α } OF BERGER