Eisenhart lift in pseudo–Euclidean space and higher rank killing tensors

2017 ◽  
Vol 14 (2) ◽  
pp. 328-330 ◽  
Author(s):  
Anton Galajinsky
Keyword(s):  
Euclidean Space ◽  
Killing Tensors ◽  
Higher Rank

scholarly journals Equidistribution of divergent orbits of the diagonal group in the space of lattices

2018 ◽  
Vol 40 (5) ◽  
pp. 1217-1237 ◽  
Author(s):  
OFIR DAVID ◽  
URI SHAPIRA
Keyword(s):  
Euclidean Space ◽  
Life Span ◽  
Compact Set ◽  
Integer Vector ◽  
Entropy Methods ◽  
Numerical Invariants ◽  
Measure Rigidity ◽  
Higher Rank

We consider divergent orbits of the group of diagonal matrices in the space of lattices in Euclidean space. We define two natural numerical invariants of such orbits: the discriminant—an integer—and the type—an integer vector. We then study the question of the limit distributional behavior of these orbits as the discriminant goes to infinity. Using entropy methods we prove that, for divergent orbits of a specific type, virtually any sequence of orbits equidistributes as the discriminant goes to infinity. Using measure rigidity for higher-rank diagonal actions, we complement this result and show that, in dimension three or higher, only very few of these divergent orbits can spend all of their life-span in a given compact set before they diverge.

scholarly journals Ricci-flat spacetimes admitting higher rank Killing tensors

2015 ◽  
Vol 744 ◽  
pp. 320-324 ◽  
Author(s):  
Marco Cariglia ◽  
Anton Galajinsky
Keyword(s):  
Killing Tensors ◽  
Ricci Flat ◽  
Flat Spacetimes ◽  
Higher Rank

scholarly journals IRREDUCIBLE KILLING TENSORS FROM THIRD RANK KILLING–YANO TENSORS

2007 ◽  
Vol 22 (18) ◽  
pp. 1309-1317 ◽  
Author(s):  
FLORIAN CATALIN POPA ◽  
OVIDIU TINTAREANU-MIRCEA
Keyword(s):  
Killing Tensor ◽  
Killing Tensors ◽  
Higher Rank

We investigate higher rank Killing–Yano tensors showing that third rank Killing–Yano tensors are not always trivial objects being possible to construct irreducible Killing tensors from them. We give as an example the Kimura IIC metric from two-rank Killing–Yano tensors to obtain a reducible Killing tensor and from third-rank Killing–Yano tensors, we obtain three Killing tensors, one reducible and two irreducible.

Symplectic capacities

2017 ◽  
Author(s):  
Dusa McDuff ◽  
Dietmar Salamon
Keyword(s):  
Euclidean Space ◽  
Generating Functions ◽  
Weinstein Conjecture ◽  
Finite Dimensional ◽  
Hofer Metric

This chapter returns to the problems which were formulated in Chapter 1, namely the Weinstein conjecture, the nonsqueezing theorem, and symplectic rigidity. These questions are all related to the existence and properties of symplectic capacities. The chapter begins by discussing some of the consequences which follow from the existence of capacities. In particular, it establishes symplectic rigidity and discusses the relation between capacities and the Hofer metric on the group of Hamiltonian symplectomorphisms. The chapter then introduces the Hofer–Zehnder capacity, and shows that its existence gives rise to a proof of the Weinstein conjecture for hypersurfaces of Euclidean space. The last section contains a proof that the Hofer–Zehnder capacity satisfies the required axioms. This proof translates the Hofer–Zehnder variational argument into the setting of (finite-dimensional) generating functions.

scholarly journals Killing tensors on tori

2017 ◽  
Vol 117 ◽  
pp. 1-6
Author(s):  
Konstantin Heil ◽  
Andrei Moroianu ◽  
Uwe Semmelmann
Keyword(s):  
Killing Tensors
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