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On eigen-values of Laplacian and curvature of Riemannian manifold

Takashi Sakai
- 01 Jan 1971 - 
- Vol. 23, Iss: 4, pp 589-603
About: 
This article is published in Tohoku Mathematical Journal.The article was published on 1971-01-01 and is currently open access. It has received 88 citations till now. The article focuses on the topics: Scalar curvature & Ricci curvature.

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Citations
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A mapping of Riemannian manifolds which preserves harmonic functions

Toru Ishihara
- 01 Jan 1979 - 
Journal ArticleDOI

Finite temperature and boundary effects in static space-times

J.S. Dowker, +1 more
- 01 May 1978 - 
TL;DR: In this article, the free energy of a massless scalar gas confined to a spatial cavity in a static space-time at a finite temperature is derived, and a high temperature expansion is presented in terms of the Minakshisundaram coefficients.
Journal ArticleDOI

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

Gerard Kennedy, +2 more
- 01 Apr 1980 - 
TL;DR: The role played by boundary contributions to the integrated quantum mechanical propogator for a finite system is emphasised in this paper, where the local stress tensor is calculated for a scalar field at finite temperature in a static spacetime with boundaries.
Journal ArticleDOI

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

Fiorenzo Bastianelli, +2 more
- 01 Feb 2000 - 
TL;DR: In this paper, the conformal anomaly in the free d = 6 superconformal (2,0) tensor multiplet theory on generic curved background is computed 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.
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Riemannian geometry as determined by the volumes of small geodesic balls

A Gray, +1 more
- 01 Jan 1979 - 
TL;DR: In this paper, the first two terms of the power series expansion for Fro(r) are computed for surfaces in RS and the coefficients of r n+~ for/r even can be expressed in terms of curvature.
References
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Curvature and the Eigenvalues of the Laplacian

H. P. McKean, +1 more
- 01 Jan 1967 - 
TL;DR: In this paper, the authors defined the spectrum of the problem of bounded regions of R d with a piecewise smooth boundary B and showed that if 0 > γ1 ≥ γ2 ≥ ≥ ≥ β3 ≥ etc.