Almost-Einstein manifolds with nonnegative isotropic curvature
- [1] Indian Institute of Science Department of Mathematics Bangalore 560012 (India)
Annales de l’institut Fourier (2010)
- Volume: 60, Issue: 7, page 2493-2501
- ISSN: 0373-0956
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topSeshadri, Harish. "Almost-Einstein manifolds with nonnegative isotropic curvature." Annales de l’institut Fourier 60.7 (2010): 2493-2501. <http://eudml.org/doc/116343>.
@article{Seshadri2010,
abstract = {Let $(M,g)$, $n \ge 4$, be a compact simply-connected Riemannian $n$-manifold with nonnegative isotropic curvature. Given $0<l\le L$, we prove that there exists $\varepsilon = \varepsilon (l,L,n)$ satisfying the following: If the scalar curvature $s$ of $g$ satisfies\[ l \le s \le L \]and the Einstein tensor satisfies\[ \Bigl \vert \mbox \{\rm Ric\}\, - \frac\{s\}\{n\}g \Bigr \vert \le \varepsilon \]then $M$ is diffeomorphic to a symmetric space of compact type.This is related to the result of S. Brendle on the metric rigidity of Einstein manifolds with nonnegative isotropic curvature.},
affiliation = {Indian Institute of Science Department of Mathematics Bangalore 560012 (India)},
author = {Seshadri, Harish},
journal = {Annales de l’institut Fourier},
keywords = {Almost-Einstein manifolds; non-negative isotropic curvature; almost-Einstein manifolds},
language = {eng},
number = {7},
pages = {2493-2501},
publisher = {Association des Annales de l’institut Fourier},
title = {Almost-Einstein manifolds with nonnegative isotropic curvature},
url = {http://eudml.org/doc/116343},
volume = {60},
year = {2010},
}
TY - JOUR
AU - Seshadri, Harish
TI - Almost-Einstein manifolds with nonnegative isotropic curvature
JO - Annales de l’institut Fourier
PY - 2010
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 7
SP - 2493
EP - 2501
AB - Let $(M,g)$, $n \ge 4$, be a compact simply-connected Riemannian $n$-manifold with nonnegative isotropic curvature. Given $0<l\le L$, we prove that there exists $\varepsilon = \varepsilon (l,L,n)$ satisfying the following: If the scalar curvature $s$ of $g$ satisfies\[ l \le s \le L \]and the Einstein tensor satisfies\[ \Bigl \vert \mbox {\rm Ric}\, - \frac{s}{n}g \Bigr \vert \le \varepsilon \]then $M$ is diffeomorphic to a symmetric space of compact type.This is related to the result of S. Brendle on the metric rigidity of Einstein manifolds with nonnegative isotropic curvature.
LA - eng
KW - Almost-Einstein manifolds; non-negative isotropic curvature; almost-Einstein manifolds
UR - http://eudml.org/doc/116343
ER -
References
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