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Journal ArticleDOI

Integral formulas in riemannian geometry

T. Willmore
- 01 Mar 1973 - 
- Vol. 5, Iss: 1, pp 124-125
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This article is published in Bulletin of The London Mathematical Society.The article was published on 1973-03-01. It has received 331 citations till now. The article focuses on the topics: Riemannian geometry & Fundamental theorem of Riemannian geometry.

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The generalized Poho{z}aev-Schoen identity and some geometric applications

Ezequiel Barbosa, +2 more
- 11 Jul 2016 - 
TL;DR: In this paper, a generalized Pohozaev-Schoen identity due to Gover and Orsted was used to obtain some rigidity results for $V$-static manifolds and generalized solitons.
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An example of Lichnerowicz-type Laplacian

Josef Mikeš, +2 more
- 01 Jul 2020 - 
TL;DR: In this article, the Sampson Laplacian was studied on covariant symmetric tensors on a Riemannian manifold, and the analytical method of proving vanishing theorems for the null space of a Laplace operator admitting Weitzenbock decomposition was proposed.
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K-contact metrics as Ricci solitons

Amalendu Ghosh, +1 more
TL;DR: Ghosh et al. as mentioned in this paper studied Ricci solitons on a Riemannian manifold whose metric is a Ricci tensor and showed that Ricci is a generalization of the Einstein metric and is defined on the manifold by ( £ V g) + 2 S(X,Y) +2 R ij projected from the space of metrics onto its quotient modulodiffeomorphisms and scalings.
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Vanishing theorems in affine, Riemannian, and Lorentz geometries

Sergey Stepanov
- 01 Feb 2007 - 
TL;DR: In this paper, the authors consider the Bochner technique for proving vanishing theorems by using Weitzenbock integral formulas, which allows them to extend the technique to pseudo-Riemannian manifolds and equiaffine connection manifolds.
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The second variation formula for exponentially harmonic maps

Leung-Fu Cheung, +1 more
- 01 Jun 1999 - 
TL;DR: In this article, it was shown that the identity map from any compact manifold to itself is always stable as an exponentially harmonic map, in contrast to the harmonic or p-harmonic cases where many such identity maps are unstable.