# Almost-Einstein manifolds with nonnegative isotropic curvature

Harish Seshadri^{[1]}

- [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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- A. Petrunin, W. Tuschmann, Diffeomorphism finiteness, positive pinching, and second homotopy, Geom. Funct. Anal. 9 (1999), 736-774 Zbl0941.53026MR1719602
- H. Seshadri, Manifolds with nonnegative isotropic curvature Zbl1197.53047MR2601346
- Peter Topping, Lectures on the Ricci flow, 325 (2006), Cambridge University Press, Cambridge Zbl1105.58013MR2265040

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