scholarly journals Hirzebruch–Kato surfaces, Deligne–Mostow’s construction, and new examples of negatively curved compact Kähler surfaces

1999 ◽  
Vol 7 (4) ◽  
pp. 755-786 ◽  
Author(s):  
Fangyang Zheng
Keyword(s):  
Negatively Curved ◽  
Kähler Surfaces ◽  
Kato Surfaces

Double-Helix Supramolecular Nanofibers Assembled from Negatively Curved Nanographenes

2021 ◽  
Author(s):  
Kenta Kato ◽  
Kiyofumi Takaba ◽  
Saori Maki-Yonekura ◽  
Nobuhiko Mitoma ◽  
Yusuke Nakanishi ◽  
...  
Keyword(s):  
Double Helix ◽  
Negatively Curved

scholarly journals A Lower Bound for the Remainder in Weyl's Law on Negatively Curved Surfaces

2007 ◽  
Vol 2007 ◽  
Author(s):  
Dmitry Jakobson ◽  
Iosif Polterovich ◽  
John A. Toth
Keyword(s):  
Lower Bound ◽  
Curved Surfaces ◽  
Weyl’S Law ◽  
Negatively Curved ◽  
Weyl's Law

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.

Negatively Curved Geometry

2019 ◽  
pp. 23-48
Author(s):  
Anne Broise-Alamichel ◽  
Jouni Parkkonen ◽  
Frédéric Paulin
Keyword(s):  
Negatively Curved

scholarly journals Cocycle superrigidity and bounded cohomology for negatively curved spaces

2004 ◽  
Vol 67 (3) ◽  
pp. 395-455 ◽  
Author(s):  
Nicolas Monod ◽  
Yehuda Shalom
Keyword(s):  
Bounded Cohomology ◽  
Curved Spaces ◽  
Negatively Curved

scholarly journals The singular terms in the fundamental matrix of crystal optics

2011 ◽  
Vol 467 (2133) ◽  
pp. 2663-2689 ◽  
Author(s):  
Peter Wagner
Keyword(s):  
Explicit Formula ◽  
Fundamental Matrix ◽  
Singular Part ◽  
Wave Surface ◽  
Crystal Optics ◽  
Cauchy Principal ◽  
Singular Terms ◽  
Negatively Curved ◽  
Principal Value ◽  
Positively Curved

We derive an explicit formula for the singular part of the fundamental matrix of crystal optics. It consists of a singularity remaining fixed at the origin x =0, of delta terms located on the positively curved parts of the wave surface, the well-known Fresnel surface and of a Cauchy principal value distribution on the negatively curved part of the wave surface.

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