A complete classification of generic singularities of geodesic flows on 2-surfaces with pseudo-Riemannian metrics

2017 ◽  
Vol 72 (3) ◽  
pp. 577-579 ◽  
Author(s):  
N G Pavlova ◽  
A O Remizov
Keyword(s):  
Riemannian Metrics ◽  
Complete Classification ◽  
Geodesic Flows ◽  
Generic Singularities

Completion of the classification of generic singularities of geodesic flows in two classes of metrics

2019 ◽  
Vol 83 (1) ◽  
pp. 104-123
Author(s):  
N. G. Pavlova ◽  
A. O. Remizov
Keyword(s):  
Geodesic Flows ◽  
Generic Singularities

Geodesic orbit Randers metrics on spheres

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Shaoxiang Zhang ◽  
Zaili Yan
Keyword(s):  
Finsler Geometry ◽  
Riemannian Metrics ◽  
Complete Classification ◽  
Invariant Metrics ◽  
Navigation Data ◽  
Randers Metrics

AbstractStudying geodesic orbit Randers metrics on spheres, we obtain a complete classification of such metrics. Our method relies upon the classification of geodesic orbit Riemannian metrics on the spheres Sn in [17] and the navigation data in Finsler geometry. We also construct some explicit U(n + 1)-invariant metrics on S2n+1 and Sp(n + 1)U(1)-invariant metrics on S4n+3.

scholarly journals Геодезически орбитальные метрики на сферах

2013 ◽  
Author(s):  
Y.G. Nikonorov
Keyword(s):  
Riemannian Metrics ◽  
Complete Classification ◽  
Invariant Metrics

In this paper, a complete classification of geodesic orbit Riemannian metrics on spheres Sn is obtained. We also construct some explicit examples of geodesic vectors for Sp(n+1)U(1)-invariant metrics on S4n+3.

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.

A Complete Classification of Curvature Collineations of Cylindrically Symmetric Static Metrics

2003 ◽  
Vol 35 (6) ◽  
pp. 1059-1076 ◽  
Author(s):  
Ashfaque H. Bokhari ◽  
Abdul R. Kashif ◽  
Asghar Qadir
Keyword(s):  
Complete Classification ◽  
Cylindrically Symmetric ◽  
Curvature Collineations
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