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A note on the almost-Schur lemma on  -dimensional Riemannian closed manifolds
Author:
Ezequiel R. Barbosa
Journal:
Proc. Amer. Math. Soc. 140 (2012), 4319-4322
MSC (2010):
Primary 53C25
Posted:
March 29, 2012
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Abstract: In this short paper, we prove a type of the almost-Schur lemma, introduced by De Lellis-Topping, on 4-dimensional Riemannian closed manifolds assuming no conditions on the Ricci tensor or the scalar curvature.
- 1.
Y. Ge, G. Wang, An almost Schur Theorem on
 -dimensional manifolds, Proc. Amer. Math. Soc. 140 (2012), pp. 1041-1044.
- 2.
C. De Lellis, P. Topping, Almost-Schur Lemma, to appear in Calc. Var. and PDE.
- 3.
Matthew
J. Gursky, The principal eigenvalue of a conformally invariant
differential operator, with an application to semilinear elliptic PDE,
Comm. Math. Phys. 207 (1999), no. 1, 131–143.
MR
1724863 (2000k:58029), http://dx.doi.org/10.1007/s002200050721
- 4.
Morio
Obata, The conjectures on conformal transformations of Riemannian
manifolds, J. Differential Geometry 6 (1971/72),
247–258. MR 0303464
(46 #2601)
- 1.
- Y. Ge, G. Wang, An almost Schur Theorem on -dimensional manifolds, Proc. Amer. Math. Soc. 140 (2012), pp. 1041-1044.
- 2.
- C. De Lellis, P. Topping, Almost-Schur Lemma, to appear in Calc. Var. and PDE.
- 3.
- M. Gursky, The principal eigenvalue of a conformally invariant differential operator, with an application to semilinear elliptic PDE, Comm. Math. Phys. 207 (1999), pp. 131-143. MR 1724863 (2000k:58029)
- 4.
- M. Obata, The conjectures on conformal transformations of Riemannian manifolds, J. Diff. Geo. 6 (1971), pp. 247-258. MR 0303464 (46:2601)
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Additional Information
Ezequiel R. Barbosa
Affiliation:
Department of Mathematics, ICEx, Universidade Federal de Minas Gerais, C.P. 702, Belo Horizonte, MG, CEP 30161-970, Brazil
Email:
ezequiel@mat.ufmg.br
DOI:
http://dx.doi.org/10.1090/S0002-9939-2012-11255-9
PII:
S 0002-9939(2012)11255-9
Keywords:
Einstein manifold,
Schur’s Theorem,
4-dimensional manifold.
Received by editor(s):
October 13, 2010
Received by editor(s) in revised form:
April 19, 2011, and May 13, 2011
Posted:
March 29, 2012
Additional Notes:
The author was partially supported by CNPq-Brazil
Communicated by:
Michael Wolf
Article copyright:
© Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
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