Rigidity Results for Self-Shrinking Surfaces in ℝ4

2021 ◽  
Vol 41 (5) ◽  
pp. 1417-1427
Author(s):  
Xuyong Jiang ◽  
Hejun Sun ◽  
Peibiao Zhao
Keyword(s):  
Rigidity Results

Complete spacelike hypersurfaces in a Robertson–Walker spacetime

2011 ◽  
Vol 151 (2) ◽  
pp. 271-282 ◽  
Author(s):  
ALMA L. ALBUJER ◽  
FERNANDA E. C. CAMARGO ◽  
HENRIQUE F. DE LIMA
Keyword(s):  
Maximum Principle ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Rigidity Results ◽  
Complete Spacelike Hypersurfaces ◽  
Uniqueness Results ◽  
Spacelike Hypersurfaces ◽  
Generalized Maximum Principle ◽  
Non Parametric

AbstractIn this paper, as a suitable application of the well-known generalized maximum principle of Omori–Yau, we obtain uniqueness results concerning to complete spacelike hypersurfaces with constant mean curvature immersed in a Robertson–Walker (RW) spacetime. As an application of such uniqueness results for the case of vertical graphs in a RW spacetime, we also get non-parametric rigidity results.

scholarly journals Remarks on Stationary and Uniformly-rotating Vortex Sheets: Rigidity Results

2021 ◽  
Author(s):  
Javier Gómez-Serrano ◽  
Jaemin Park ◽  
Jia Shi ◽  
Yao Yao
Keyword(s):  
Angular Velocity ◽  
Disjoint Union ◽  
Vortex Sheet ◽  
Vortex Sheets ◽  
Smooth Curves ◽  
Rigidity Results ◽  
Positive Vorticity ◽  
Constant Vorticity ◽  
Concentric Circles ◽  
Finite Disjoint Union

AbstractIn this paper, we show that the only solution of the vortex sheet equation, either stationary or uniformly rotating with negative angular velocity $$\Omega $$ Ω , such that it has positive vorticity and is concentrated in a finite disjoint union of smooth curves with finite length is the trivial one: constant vorticity amplitude supported on a union of nested, concentric circles. The proof follows a desingularization argument and a calculus of variations flavor.

Influence of the Torsional Rigidity of Transverse Stiffeners upon the Shear Buckling of Stiffened Plates

1964 ◽  
Vol 15 (2) ◽  
pp. 198-202 ◽  
Author(s):  
K. C. Rockey ◽  
I. T. Cook
Keyword(s):  
Flexural Rigidity ◽  
Torsional Rigidity ◽  
Stiffened Plates ◽  
Simply Supported ◽  
Rigidity Results ◽  
Buckling Resistance ◽  
Shear Buckling

SummaryThe paper provides relationships between the buckling resistance of simply-supported transversely stiffened plates and the flexural rigidity of the stiffeners for various values of the ratio of torsional rigidity to nexural rigidity. Results are presented for four different stiffener spacings.

Effect of Bending Rigidity of Stringers Upon Stress Distribution in Reinforced Monocoque Cylinder Under Concentrated Transverse Loads

1948 ◽  
Vol 15 (1) ◽  
pp. 30-36
Author(s):  
Robert S. Levy
Keyword(s):  
Stress Distribution ◽  
Present Method ◽  
Load Application ◽  
Shear Stresses ◽  
Bending Rigidity ◽  
Work Analysis ◽  
Rigidity Results ◽  
Transverse Loads ◽  
Strain Rosette ◽  
Good Agreement

Abstract Least-work analysis of stress distribution in a reinforced circular monocoque cylinder is extended to determine the effect of bending resistant stringers located at the points of application of concentrated transverse loads. Calculations for a numerical example, with applied loads diametrically opposed, indicate that neglect of stringer bending rigidity results in calculated maximum shear stresses approximately 20 per cent conservative in the fields of load application and 50 per cent unsafe in an intermediate field. Further calculations indicate that the bending rigidity of the stringer has less effect when all loads are applied at the same circumferential location. Comparison of shear stresses, calculated by the present method with strain-rosette readings, indicate good agreement.

Ricci almost solitons and contact geometry

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Amalendu Ghosh
Keyword(s):  
Vector Field ◽  
Contact Manifold ◽  
Ricci Soliton ◽  
Jacobi Field ◽  
Reeb Vector ◽  
Potential Vector ◽  
Reeb Vector Field ◽  
Rigidity Results ◽  
Parallel Ricci Tensor ◽  
Potential Vector Field

Abstract We prove that on a K-contact manifold, a Ricci almost soliton is a Ricci soliton if and only if the potential vector field V is a Jacobi field along the Reeb vector field ξ. Then we study contact metric as a Ricci almost soliton with parallel Ricci tensor. To this end, we consider Ricci almost solitons whose potential vector field is a contact vector field and prove some rigidity results.

scholarly journals LINEAR WEINGARTEN HYPERSURFACES IN A REAL SPACE FORM

2010 ◽  
Vol 52 (3) ◽  
pp. 635-648 ◽  
Author(s):  
SHICHANG SHU
Keyword(s):  
Space Form ◽  
Real Space ◽  
Principal Curvatures ◽  
Riemannian Product ◽  
Rigidity Results ◽  
Linear Weingarten Hypersurfaces

AbstractIn this paper, we investigate linear Weingarten hypersurfaces with two distinct principal curvatures in a real space form Mn+1(c), we obtain two rigidity results and give some characterization of the Riemannian product Sk(a) × Sn−k($\sqrt{1-a^2})\$), 1 ≤ k ≤ n − 1 in Mn+1(c)(c = 1), the Riemannian product Rk × Sn−k(a), 1 ≤ k ≤ n −1 in Mn+1(c)(c = 0) and the Riemannian product Hk(tanh2 ρ−1) × Sn−k(coth2 ρ−1), 1 ≤ k ≤ n −1 in Mn+1(c)(c = −1).

ON HARMONIC AND PSEUDOHARMONIC MAPS FROM PSEUDO-HERMITIAN MANIFOLDS

2017 ◽  
Vol 234 ◽  
pp. 170-210 ◽  
Author(s):  
TIAN CHONG ◽  
YUXIN DONG ◽  
YIBIN REN ◽  
GUILIN YANG
Keyword(s):  
Riemannian Manifolds ◽  
Harmonic Maps ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Rigidity Results ◽  
Hermitian Manifolds

In this paper, we give some rigidity results for both harmonic and pseudoharmonic maps from pseudo-Hermitian manifolds into Riemannian manifolds or Kähler manifolds. Some foliated results, pluriharmonicity and Siu–Sampson type results are established for both harmonic maps and pseudoharmonic maps.

scholarly journals Some OE- and W⁎-rigidity results for actions by wreath product groups

2012 ◽  
Vol 263 (11) ◽  
pp. 3422-3448 ◽  
Author(s):  
Ionut Chifan ◽  
Sorin Popa ◽  
James Owen Sizemore
Keyword(s):  
Wreath Product ◽  
Rigidity Results
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