scholarly journals Some minimal submanifolds generalizing the Clifford torus

2018 ◽  
Vol 291 (17-18) ◽  
pp. 2536-2542
Author(s):  
Jaigyoung Choe ◽  
Jens Hoppe
Keyword(s):  
Minimal Submanifolds ◽  
Clifford Torus

scholarly journals PINCHING THEOREMS FOR TOTALLY REAL MINIMAL SUBMANIFOLDS INCPn

2009 ◽  
Vol 51 (2) ◽  
pp. 331-339
Author(s):  
CENGİZHAN MURATHAN ◽  
CİHAN ÖZGÜR
Keyword(s):  
Projective Space ◽  
Scalar Curvature ◽  
Minimal Submanifolds ◽  
Minimal Submanifold ◽  
Real Projective Space ◽  
Clifford Torus ◽  
Open Part ◽  
The Real ◽  
Totally Real

AbstractLetMbe ann-dimensional totally real minimal submanifold inCPn. We prove that ifMis semi-parallel and the scalar curvature τ,$\frac{-(n-1)(n-2)(n+1)}{2}\leq \tau \leq 0$, thenMis an open part of the Clifford torusTn⊂CPn. IfMis semi-parallel and the scalar curvature τ,$n(n-1)\leq \tau \leq \frac{n^{3}-3n+2}{2}$, thenMis an open part of the real projective spaceRPn.

A characterization of the Clifford Torus

1999 ◽  
Vol 48 (3) ◽  
pp. 537-540 ◽  
Author(s):  
I. Guadalupe ◽  
Aldir Brasil Junior ◽  
J. A. Delgado
Keyword(s):  
Clifford Torus

scholarly journals On stable compact minimal submanifolds

2013 ◽  
Vol 142 (2) ◽  
pp. 651-658
Author(s):  
Francisco Torralbo ◽  
Francisco Urbano
Keyword(s):  
Minimal Submanifolds

Basic Geometric Constructions

2021 ◽  
pp. 217-226
Author(s):  
Mark Powell ◽  
Arunima Ray
Keyword(s):  
Dimensional Space ◽  
Intersection Point ◽  
Important Application ◽  
Geometric Constructions ◽  
Clifford Torus ◽  
The Cost ◽  
Regular Homotopy ◽  
Associated Surfaces

Basic geometric constructions, including tubing, boundary twisting, pushing down intersections, and contraction followed by push-off are presented. These moves are used repeatedly later in the proof. New, detailed pictures illustrating these constructions are provided. The Clifford torus at an intersection point between two surfaces in 4-dimensional space is described. The chapter closes with an important application of some of these moves called the Geometric Casson Lemma. This lemma upgrades algebraically dual spheres to geometrically dual spheres, at the cost of introducing more self-intersections. It is also shown that an immersed Whitney move is a regular homotopy of the associated surfaces.

Minimal submanifolds in general (α,β)-spaces

2013 ◽  
Vol 108 (1) ◽  
pp. 43-59 ◽  
Author(s):  
Songting Yin ◽  
Qun He ◽  
Dinghe Xie
Keyword(s):  
Minimal Submanifolds
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