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 A characterization of complete Riemannian manifolds minimally immersed in the unit sphere

1993 ◽  
Vol 131 ◽  
pp. 127-133 ◽  
Author(s):  
Qing-Ming Cheng
Keyword(s):  
Riemannian Manifold ◽  
Fundamental Form ◽  
Riemannian Manifolds ◽  
Unit Sphere ◽  
Second Fundamental Form ◽  
Clifford Torus ◽  
Veronese Surface ◽  
The Second Fundamental Form ◽  
Complete Riemannian Manifolds

Let Mn be an n-dimensional Riemannian manifold minimally immersed in the unit sphere Sn+p (1) of dimension n + p. When Mn is compact, Chern, do Carmo and Kobayashi [1] proved that if the square ‖h‖2 of length of the second fundamental form h in Mn is not more than , then either Mn is totallygeodesic, or Mn is the Veronese surface in S4 (1) or Mn is the Clifford torus .In this paper, we generalize the results due to Chern, do Carmo and Kobayashi [1] to complete Riemannian manifolds.

scholarly journals Characterization of Clifford Torus in Three-Spheres

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 718
Author(s):  
Dong-Soo Kim ◽  
Young Ho Kim ◽  
Jinhua Qian
Keyword(s):  
Laplace Operator ◽  
Unit Sphere ◽  
Three Dimensional ◽  
Gauss Map ◽  
Dimensional Sphere ◽  
Clifford Torus ◽  
Closed Surfaces ◽  
Dimensional Unit ◽  
The Laplace Operator

We characterize spheres and the tori, the product of the two plane circles immersed in the three-dimensional unit sphere, which are associated with the Laplace operator and the Gauss map defined by the elliptic linear Weingarten metric defined on closed surfaces in the three-dimensional sphere.

A characterization of the Clifford torus

2005 ◽  
Vol 85 (2) ◽  
pp. 175-182 ◽  
Author(s):  
Theodoros Vlachos
Keyword(s):  
Clifford Torus

scholarly journals A new characterization of the Clifford torus in S3 via the quadric representation

1994 ◽  
Vol 20 (2) ◽  
pp. 213-224
Author(s):  
Manuel BARROS ◽  
Oscar Jesus GARA
Keyword(s):  
Clifford Torus

scholarly journals A characterization of the Clifford torus

1999 ◽  
Vol 127 (3) ◽  
pp. 819-828 ◽  
Author(s):  
Qing-Ming Cheng ◽  
Susumu Ishikawa
Keyword(s):  
Clifford Torus

A new characterization of Clifford torus

2017 ◽  
Vol 91 (1-2) ◽  
pp. 133-142
Author(s):  
Fabio R. dos Santos ◽  
Henrique F. de Lima ◽  
Marco A.~L. Velasquez
Keyword(s):  
Clifford Torus

scholarly journals Hypersurfaces with constant mean curvature and two principal curvatures in n+1

2004 ◽  
Vol 76 (3) ◽  
pp. 489-497 ◽  
Author(s):  
Luis J. Alías ◽  
Sebastião C. de Almeida ◽  
Aldir Brasil Jr.
Keyword(s):  
Fundamental Form ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Integral Formula ◽  
Second Fundamental Form ◽  
Euclidean Sphere ◽  
Principal Curvatures ◽  
Clifford Torus ◽  
The Second Fundamental Form

In this paper we consider compact oriented hypersurfaces M with constant mean curvature and two principal curvatures immersed in the Euclidean sphere. In the minimal case, Perdomo (Perdomo 2004) andWang (Wang 2003) obtained an integral inequality involving the square of the norm of the second fundamental form of M, where equality holds only if M is the Clifford torus. In this paper, using the traceless second fundamental form of M, we extend the above integral formula to hypersurfaces with constant mean curvature and give a new characterization of the H(r)-torus.

Morphological Characterization of Mycobacteriophage R1

1974 ◽  
Vol 32 ◽  
pp. 254-255
Author(s):  
B. L. Soloff ◽  
T. A. Rado
Keyword(s):  
Carbon Source ◽  
Stationary Phase ◽  
Growth Phase ◽  
Minimal Medium ◽  
Morphological Characterization ◽  
Logarithmic Growth Phase ◽  
Complete Lysis ◽  
Lysogenic Culture ◽  
Logarithmic Growth

Mycobacteriophage R1 was originally isolated from a lysogenic culture of M. butyricum. The virus was propagated on a leucine-requiring derivative of M. smegmatis, 607 leu−, isolated by nitrosoguanidine mutagenesis of typestrain ATCC 607. Growth was accomplished in a minimal medium containing glycerol and glucose as carbon source and enriched by the addition of 80 μg/ ml L-leucine. Bacteria in early logarithmic growth phase were infected with virus at a multiplicity of 5, and incubated with aeration for 8 hours. The partially lysed suspension was diluted 1:10 in growth medium and incubated for a further 8 hours. This permitted stationary phase cells to re-enter logarithmic growth and resulted in complete lysis of the culture.

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