scholarly journals A Note on Maximal Symmetry Rank, Quasipositive Curvature, and Low Dimensional Manifolds

2014 ◽  
pp. 45-55 ◽  
Author(s):  
Fernando Galaz-Garcia
Keyword(s):  
Maximal Symmetry ◽  
Low Dimensional ◽  
Symmetry Rank

Torus actions, maximality, and non-negative curvature

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Christine Escher ◽  
Catherine Searle
Keyword(s):  
Negative Curvature ◽  
Torus Action ◽  
Maximal Symmetry ◽  
Curved Manifolds ◽  
Negatively Curved ◽  
Product Of Spheres ◽  
Rank Conjecture ◽  
Simply Connected ◽  
Symmetry Rank ◽  
Special Case

Abstract Let ℳ 0 n {\mathcal{M}_{0}^{n}} be the class of closed, simply connected, non-negatively curved Riemannian n-manifolds admitting an isometric, effective, isotropy-maximal torus action. We prove that if M ∈ ℳ 0 n {M\in\mathcal{M}_{0}^{n}} , then M is equivariantly diffeomorphic to the free, linear quotient by a torus of a product of spheres of dimensions greater than or equal to 3. As a special case, we then prove the Maximal Symmetry Rank Conjecture for all M ∈ ℳ 0 n {M\in\mathcal{M}_{0}^{n}} . Finally, we show the Maximal Symmetry Rank Conjecture for simply connected, non-negatively curved manifolds holds for dimensions less than or equal to 9 without additional assumptions on the torus action.

scholarly journals Non-negatively Curved 6-Manifolds with Almost Maximal Symmetry Rank

2018 ◽  
Vol 29 (1) ◽  
pp. 1002-1017
Author(s):  
Christine Escher ◽  
Catherine Searle
Keyword(s):  
Maximal Symmetry ◽  
Negatively Curved ◽  
Symmetry Rank

scholarly journals Positively curved manifolds with maximal symmetry-rank

1994 ◽  
Vol 91 (1-3) ◽  
pp. 137-142 ◽  
Author(s):  
Karsten Grove ◽  
Catherine Searle
Keyword(s):  
Maximal Symmetry ◽  
Curved Manifolds ◽  
Positively Curved ◽  
Symmetry Rank

scholarly journals Nonnegatively curved 5–manifolds with almost maximal symmetry rank

2014 ◽  
Vol 18 (3) ◽  
pp. 1397-1435 ◽  
Author(s):  
Fernando Galaz-Garcia ◽  
Catherine Searle
Keyword(s):  
Maximal Symmetry ◽  
Symmetry Rank

Electroabsorption in low-dimensional and bulk-like Zn1−xCdxSe

1998 ◽  
Vol 184-185 (1-2) ◽  
pp. 706-709 ◽  
Author(s):  
W Ebeling
Keyword(s):  
Low Dimensional

The Maximal Subgroups of the Low-Dimensional Finite Classical Groups

2009 ◽  
Author(s):  
John N. Bray ◽  
Derek F. Holt ◽  
Colva M. Roney-Dougal
Keyword(s):  
Maximal Subgroups ◽  
Classical Groups ◽  
Finite Classical Groups ◽  
Low Dimensional
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