scholarly journals Complete classification of surfaces with a canonical principal direction in the Euclidean space % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqipC0xg9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Wqpe0x % c9q8qqaqFn0dXdir-xcvk9pIe9q8qqaq-dir-f0-yqaqVeLsFr0-vr % 0-vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaatuuDJXwAK1 % uy0HMmaeHbfv3ySLgzG0uy0HgiuD3BaGqbaiab-ri8fbaa!4553! $$ \mathbb{E} $$ 3

2011 ◽  
Vol 9 (2) ◽  
pp. 378-389 ◽  
Author(s):  
Marian Ioan Munteanu ◽  
Ana Irina Nistor
Keyword(s):  
Euclidean Space ◽  
Principal Direction ◽  
Complete Classification ◽  
Canonical Principal Direction

scholarly journals BIHARMONIC CURVES INTO QUADRICS

2014 ◽  
Vol 57 (1) ◽  
pp. 131-141 ◽  
Author(s):  
S. MONTALDO ◽  
A. RATTO
Keyword(s):  
Euclidean Space ◽  
Three Dimensional ◽  
Algebraic Method ◽  
Polynomial Equation ◽  
Complete Classification ◽  
Dimensional Euclidean Space ◽  
Implicit Surface ◽  
Biharmonic Curves ◽  
Real Quadrics

AbstractWe develop an essentially algebraic method to study biharmonic curves into an implicit surface. Although our method is rather general, it is especially suitable to study curves in surfaces defined by a polynomial equation: In particular, we use it to give a complete classification of biharmonic curves in real quadrics of the three-dimensional Euclidean space.

New classification results on surfaces with a canonical principal direction in the Minkowski 3-space

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6023-6040 ◽  
Author(s):  
Alev Kelleci ◽  
Mahmut Ergüt ◽  
Nurettin Turgay
Keyword(s):  
Principal Direction ◽  
New Classification ◽  
Constant Direction ◽  
Canonical Principal Direction

In this paper, wecharacterize and classify all surfaces endowed with canonical principal direction relative to a space-like and light-like, constant direction in the Minkowski 3-space.

scholarly journals Multiplicative automatic sequences

2021 ◽  
Author(s):  
Jakub Konieczny ◽  
Mariusz Lemańczyk ◽  
Clemens Müllner
Keyword(s):  
Complete Classification ◽  
Automatic Sequences ◽  
Complex Valued

AbstractWe obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.

scholarly journals Characteristic cohomology and observables in higher spin gravity

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Alexey Sharapov ◽  
Evgeny Skvortsov
Keyword(s):  
Higher Spin Gravity ◽  
Complete Classification ◽  
Gravity Models ◽  
Simons Theory ◽  
Surface Charges ◽  
Higher Spin ◽  
Dynamical Invariants ◽  
Chern Simons ◽  
Conserved Currents

Abstract We give a complete classification of dynamical invariants in 3d and 4d Higher Spin Gravity models, with some comments on arbitrary d. These include holographic correlation functions, interaction vertices, on-shell actions, conserved currents, surface charges, and some others. Surprisingly, there are a good many conserved p-form currents with various p. The last fact, being in tension with ‘no nontrivial conserved currents in quantum gravity’ and similar statements, gives an indication of hidden integrability of the models. Our results rely on a systematic computation of Hochschild, cyclic, and Chevalley-Eilenberg cohomology for the corresponding higher spin algebras. A new invariant in Chern-Simons theory with the Weyl algebra as gauge algebra is also presented.

scholarly journals Nil-clean quadratic elements

2017 ◽  
Vol 16 (10) ◽  
pp. 1750197 ◽  
Author(s):  
Janez Šter
Keyword(s):  
Complete Classification ◽  
Strong Condition ◽  
Clean Rings

We provide a strong condition holding for nil-clean quadratic elements in any ring. In particular, our result implies that every nil-clean involution in a ring is unipotent. As a consequence, we give a complete classification of weakly nil-clean rings introduced recently in [Breaz, Danchev and Zhou, Rings in which every element is either a sum or a difference of a nilpotent and an idempotent, J. Algebra Appl. 15 (2016) 1650148, doi: 10.1142/S0219498816501486].

Ricci inheritance collineations in Bianchi type II spacetime

2016 ◽  
Vol 31 (17) ◽  
pp. 1650102 ◽  
Author(s):  
Tahir Hussain ◽  
Sumaira Saleem Akhtar ◽  
Ashfaque H. Bokhari ◽  
Suhail Khan
Keyword(s):  
Lie Algebra ◽  
Ricci Tensor ◽  
Bianchi Type ◽  
Complete Classification ◽  
Type Ii

In this paper, we present a complete classification of Bianchi type II spacetime according to Ricci inheritance collineations (RICs). The RICs are classified considering cases when the Ricci tensor is both degenerate as well as non-degenerate. In case of non-degenerate Ricci tensor, it is found that Bianchi type II spacetime admits 4-, 5-, 6- or 7-dimensional Lie algebra of RICs. In the case when the Ricci tensor is degenerate, majority cases give rise to infinitely many RICs, while remaining cases admit finite RICs given by 4, 5 or 6.

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