scholarly journals Local rigidity, bifurcation, and stability of $H_f$-hypersurfaces in weighted Killing warped products

2021 ◽  
Vol 65 ◽  
pp. 363-388
Author(s):  
Marco A. L. Velásquez ◽  
Henrique F. de Lima ◽  
André F. A. Ramalho
Keyword(s):  
Warped Products ◽  
Local Rigidity ◽  
Bifurcation And Stability

Bifurcation and local rigidity of constant second mean curvature hypersurfaces in Riemannian warped products

2020 ◽  
Vol 197 ◽  
pp. 111865
Author(s):  
Marco A.L. Velásquez ◽  
André F.A. Ramalho ◽  
Jonatan F. da Silva ◽  
Jobson Q. Oliveira
Keyword(s):  
Mean Curvature ◽  
Warped Products ◽  
Local Rigidity

Curvature inequalities for C-totally real doubly warped products of locally conformal almost cosymplectic manifolds

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6449-6459 ◽  
Author(s):  
Akram Ali ◽  
Siraj Uddin ◽  
Wan Othman ◽  
Cenap Ozel
Keyword(s):  
Sectional Curvature ◽  
Mean Curvature ◽  
Warped Product ◽  
Warped Products ◽  
Equality Case ◽  
Cosymplectic Manifolds ◽  
Almost Cosymplectic Manifold ◽  
Locally Conformal ◽  
Totally Real ◽  
Optimal Inequalities

In this paper, we establish some optimal inequalities for the squared mean curvature in terms warping functions of a C-totally real doubly warped product submanifold of a locally conformal almost cosymplectic manifold with a pointwise ?-sectional curvature c. The equality case in the statement of inequalities is also considered. Moreover, some applications of obtained results are derived.

Pointwise pseudo-slant submanifolds of a Kenmotsu manifold

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5833-5853 ◽  
Author(s):  
Viqar Khan ◽  
Mohammad Shuaib
Keyword(s):  
Present Article ◽  
Warped Product ◽  
Shape Operator ◽  
Warped Products ◽  
Canonical Structure ◽  
Slant Submanifold ◽  
Kenmotsu Manifold ◽  
Slant Submanifolds ◽  
Kenmotsu Manifolds

In the present article, we have investigated pointwise pseudo-slant submanifolds of Kenmotsu manifolds and have sought conditions under which these submanifolds are warped products. To this end first, it is shown that these submanifolds can not be expressed as non-trivial doubly warped product submanifolds. However, as there exist non-trivial (single) warped product submanifolds of a Kenmotsu manifold, we have worked out characterizations in terms of a canonical structure T and the shape operator under which a pointwise pseudo slant submanifold of a Kenmotsu manifold reduces to a warped product submanifold.

scholarly journals Local rigidity for actions of Kazhdan groups on noncommutative Lp-spaces

2015 ◽  
Vol 26 (08) ◽  
pp. 1550064
Author(s):  
Bachir Bekka
Keyword(s):  
Von Neumann Algebra ◽  
Regular Representation ◽  
Von Neumann ◽  
Lp Spaces ◽  
Local Rigidity ◽  
Left Regular Representation ◽  
Left Regular ◽  
Property T ◽  
Finite Factor ◽  
Finite Index Subgroup

Let Γ be a discrete group and 𝒩 a finite factor, and assume that both have Kazhdan's Property (T). For p ∈ [1, +∞), p ≠ 2, let π : Γ →O(Lp(𝒩)) be a homomorphism to the group O(Lp(𝒩)) of linear bijective isometries of the Lp-space of 𝒩. There are two actions πl and πr of a finite index subgroup Γ+ of Γ by automorphisms of 𝒩 associated to π and given by πl(g)x = (π(g) 1)*π(g)(x) and πr(g)x = π(g)(x)(π(g) 1)* for g ∈ Γ+ and x ∈ 𝒩. Assume that πl and πr are ergodic. We prove that π is locally rigid, that is, the orbit of π under O(Lp(𝒩)) is open in Hom (Γ, O(Lp(𝒩))). As a corollary, we obtain that, if moreover Γ is an ICC group, then the embedding g ↦ Ad (λ(g)) is locally rigid in O(Lp(𝒩(Γ))), where 𝒩(Γ) is the von Neumann algebra generated by the left regular representation λ of Γ.

scholarly journals A method for validating the accuracy of NMR protein structures

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Nicholas J. Fowler ◽  
Adnan Sljoka ◽  
Mike P. Williamson
Keyword(s):  
Secondary Structure ◽  
Crystal Structures ◽  
Protein Structures ◽  
Random Coil ◽  
Local Rigidity ◽  
Correlation Score ◽  
Nmr Structures ◽  
Explicit Solvent ◽  
Structure Ensemble ◽  
Better Than

AbstractWe present a method that measures the accuracy of NMR protein structures. It compares random coil index [RCI] against local rigidity predicted by mathematical rigidity theory, calculated from NMR structures [FIRST], using a correlation score (which assesses secondary structure), and an RMSD score (which measures overall rigidity). We test its performance using: structures refined in explicit solvent, which are much better than unrefined structures; decoy structures generated for 89 NMR structures; and conventional predictors of accuracy such as number of restraints per residue, restraint violations, energy of structure, ensemble RMSD, Ramachandran distribution, and clashscore. Restraint violations and RMSD are poor measures of accuracy. Comparisons of NMR to crystal structures show that secondary structure is equally accurate, but crystal structures are typically too rigid in loops, whereas NMR structures are typically too floppy overall. We show that the method is a useful addition to existing measures of accuracy.

scholarly journals Local rigidity of Schottky maps

2014 ◽  
Vol 142 (12) ◽  
pp. 4321-4332 ◽  
Author(s):  
Sergei Merenkov
Keyword(s):  
Local Rigidity
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