Involutions fixing an arbitrary product of spheres and a point

1996 ◽  
Vol 89 (1) ◽  
pp. 471-474 ◽  
Author(s):  
Pedro L. Q. Pergher
Keyword(s):  
Product Of Spheres ◽  
Arbitrary Product

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.

Quantum Discord in any Mixture of Two Bi-Qubit Arbitrary Product States

2013 ◽  
Vol 60 (6) ◽  
pp. 667-672 ◽  
Author(s):  
Sheng-Fang Wang ◽  
Yi-Min Liu ◽  
Guo-Feng Li ◽  
Xian-Song Liu ◽  
Zhan-Jun Zhang
Keyword(s):  
Quantum Discord ◽  
Arbitrary Product

scholarly journals Differentiable structures on a generalized product of spheres

1987 ◽  
Vol 10 (2) ◽  
pp. 217-226
Author(s):  
Samuel Omoloye Ajala
Keyword(s):  
Complete Classification ◽  
Smooth Structures ◽  
Product Of Spheres

In this paper, we give a complete classification of smooth structures on a generalized product of spheres. Ihe result generalizes our result in [1] and R. de Sapio's result in [2].

scholarly journals Diffeomorphisms of a product of spheres and embedded spheres

2002 ◽  
Vol 123 (3) ◽  
pp. 471-478 ◽  
Author(s):  
Laércio Aparecido Lucas ◽  
Osamu Saeki
Keyword(s):  
Product Of Spheres
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