scholarly journals Isometric immersions of Euclidean plane into Euclidean 4-space with vanishing normal curvature

2009 ◽  
Vol 61 (4) ◽  
pp. 523-550
Author(s):  
Hiroshi Mori ◽  
Norio Shimakura
Keyword(s):  
Euclidean Plane ◽  
Normal Curvature ◽  
Isometric Immersions

Isometric immersions of a Euclidean plane in Lobachevskii space

1971 ◽  
Vol 10 (3) ◽  
pp. 619-622 ◽  
Author(s):  
Yu. A. Volkov ◽  
S. M. Vladimirova
Keyword(s):  
Euclidean Plane ◽  
Isometric Immersions ◽  
Lobachevskii Space

scholarly journals Cutoff AdS3 versus $$ T\overline{T} $$ CFT2 in the large central charge sector: correlators of energy-momentum tensor

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yi Li ◽  
Yang Zhou
Keyword(s):  
Field Theory ◽  
Euclidean Plane ◽  
Energy Momentum Tensor ◽  
Central Charge ◽  
Momentum Tensor ◽  
Two Dimensional ◽  
Conformal Field ◽  
Operator Identity ◽  
Pure Gravity ◽  
Charge Sector

Abstract In this article we probe the proposed holographic duality between $$ T\overline{T} $$ T T ¯ deformed two dimensional conformal field theory and the gravity theory of AdS3 with a Dirichlet cutoff by computing correlators of energy-momentum tensor. We focus on the large central charge sector of the $$ T\overline{T} $$ T T ¯ CFT in a Euclidean plane and a sphere, and compute the correlators of energy-momentum tensor using an operator identity promoted from the classical trace relation. The result agrees with a computation of classical pure gravity in Euclidean AdS3 with the corresponding cutoff surface, given a holographic dictionary which identifies gravity parameters with $$ T\overline{T} $$ T T ¯ CFT parameters.

scholarly journals On Negligible and Absolutely Nonmeasurable Subsets of the Euclidean Plane

2004 ◽  
Vol 11 (3) ◽  
pp. 479-487
Author(s):  
A. Kharazishvili
Keyword(s):  
Euclidean Plane ◽  
Identity Transformation ◽  
Extension Problem ◽  
Measure Extension ◽  
Nonmeasurable Set

Abstract The notions of a negligible set and of an absolutely nonmeasurable set are introduced and discussed in connection with the measure extension problem. In particular, it is demonstrated that there exist subsets of the plane 𝐑2 which are 𝑇2-negligible and, simultaneously, 𝐺-absolutely nonmeasurable. Here 𝑇2 denotes the group of all translations of 𝐑2 and 𝐺 denotes the group generated by {𝑔} ∪ 𝑇2, where 𝑔 is an arbitrary rotation of 𝐑2 distinct from the identity transformation and all central symmetries of 𝐑2.

Compositions of isometric immersions¶in higher codimension

2001 ◽  
Vol 105 (4) ◽  
pp. 507-517 ◽  
Author(s):  
Marcos Dajczer ◽  
Luis A. Florit
Keyword(s):  
Isometric Immersions

Grade of Service Steiner Minimum Trees in the Euclidean Plane

Algorithmica ◽  
2001 ◽  
Vol 31 (4) ◽  
pp. 479-500 ◽  
Author(s):  
Xue ◽  
-H. Lin ◽  
-Z. Du
Keyword(s):  
Euclidean Plane ◽  
Grade Of Service

scholarly journals How to Collect Balls Moving in the Euclidean Plane

2004 ◽  
Vol 91 ◽  
pp. 229-245 ◽  
Author(s):  
Yuichi Asahiro ◽  
Takashi Horiyama ◽  
Kazuhisa Makino ◽  
Hirotaka Ono ◽  
Toshinori Sakuma ◽  
...  
Keyword(s):  
Euclidean Plane
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