SCALAR CURVATURE ESTIMATES FOR COMPACT SYMMETRIC SPACES
By S. Goette, U. Semmelmann. 2000
65 citations recorded by the source corpus.
Abstract We establish extremality of Riemannian metrics g with non-negative curvature operator on symmetric spaces M=G/K of compact type with rkG−rkK⩽1. Let ḡ be another metric with scalar curvature κ , such that g ⩾g on 2-vectors. We show that κ ⩾κ everywhere on M implies κ =κ . Under an additional condition on the Ricci curvature of g, κ ⩾κ even implies g =g . We also study area-non-increasing spin maps onto such Riemannian manifolds.
Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/3635c8ed39a677be35ca26dd9bc26db3becdf670
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In Applied Mathematics
In Astronomy and Astrophysics
In Geometry and Topology
- Misha Gromov
- Assaf Naor
- Yann Ollivier
- Alexander Lubotzky
- Damian Osajda
- Denis V. Osin
- Richard Bamler
- Larry Guth
Citations in the corpus
- Dirac and Plateau billiards in domains with corners (2014, background): “The concepts of the dihedral extremality as well as the extremality of manifolds with positive scalar curvature that was studied in [13, 19, 32, 41] are embraced by the following”
- Four Lectures on Scalar Curvature (2019, background): “Also notice that the doubling property for mean convex manifolds with boundaries (see [GL(fundamental group) 1980]) allows a reduction of the Geroch Conjecture and of similar more general results to the Goette-Semmelmann theorem [GS 2002] concerning extremality/rigidity of the metrics g with positiv”