Sufficient conditions for periodicity of a Killing vector field

In this article, we study Jacobi-type vector fields on Riemannian manifolds. A Killing vector field is a Jacobi-type vector field while the converse is not true, leading to a natural question of finding conditions under which a Jacobi-type vector field is Killing. In this article, we first prove that every Jacobi-type vector field on a compact Riemannian manifold is Killing. Then, we find several necessary and sufficient conditions for a Jacobi-type vector field to be a Killing vector field on non-compact Riemannian manifolds. Further, we derive some characterizations of Euclidean spaces in terms of Jacobi-type vector fields. Finally, we provide examples of Jacobi-type vector fields on non-compact Riemannian manifolds, which are non-Killing.

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On the geometry of Killing vector field

Uzbek Mathematical Journal ◽

10.29229/uzmj.2019-2-7 ◽

2019 ◽

Vol 2019 (2) ◽

pp. 62-67

Author(s):

R.A. Ilyasova

Keyword(s):

Vector Field ◽

Killing Vector ◽

Killing Vector Field

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Some Properties of Para-Sasakian Manifolds

Science & Technology Journal ◽

10.22232/stj.2017.05.02.01 ◽

2017 ◽

Vol 5 (2) ◽

pp. 73-78

Author(s):

Jay Prakash Singh ◽

Keyword(s):

Vector Field ◽

Killing Vector ◽

Sasakian Manifold ◽

Subject Classification ◽

Killing Vector Field ◽

Sasakian Manifolds ◽

Geometric Properties ◽

Paper Author

In this paper author present an investigation of some differential geometric properties of Para-Sasakian manifolds. Condition for a vector field to be Killing vector field in Para-Sasakian manifold is obtained. Mathematics Subject Classification (2010). 53B20, 53C15.

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Cohomological localization of $$ \mathcal{N} $$ = 2 gauge theories with matter

Journal of High Energy Physics ◽

10.1007/jhep09(2020)133 ◽

2020 ◽

Vol 2020 (9) ◽

Author(s):

Guido Festuccia ◽

Anastasios Gorantis ◽

Antonio Pittelli ◽

Konstantina Polydorou ◽

Lorenzo Ruggeri

Keyword(s):

Vector Field ◽

Extended Supersymmetry ◽

General Framework ◽

Gauge Theories ◽

Killing Vector ◽

Killing Vector Field ◽

Explicit Result ◽

Yang Mills ◽

Self Duality ◽

Witten Theory

Abstract We construct a large class of gauge theories with extended supersymmetry on four-dimensional manifolds with a Killing vector field and isolated fixed points. We extend previous results limited to super Yang-Mills theory to general $$ \mathcal{N} $$ N = 2 gauge theories including hypermultiplets. We present a general framework encompassing equivariant Donaldson-Witten theory and Pestun’s theory on S4 as two particular cases. This is achieved by expressing fields in cohomological variables, whose features are dictated by supersymmetry and require a generalized notion of self-duality for two-forms and of chirality for spinors. Finally, we implement localization techniques to compute the exact partition function of the cohomological theories we built up and write the explicit result for manifolds with diverse topologies.

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The exterior derivative as a Killing vector field

Israel Journal of Mathematics ◽

10.1007/bf02761099 ◽

1996 ◽

Vol 93 (1) ◽

pp. 157-170 ◽

Cited By ~ 7

Author(s):

J. Monterde ◽

O. A. Sánchez-Valenzuela

Keyword(s):

Vector Field ◽

Killing Vector ◽

Killing Vector Field ◽

Exterior Derivative

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Change in Hamiltonian general relativity from the lack of a time-like Killing vector field

Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics ◽

10.1016/j.shpsb.2014.05.007 ◽

2014 ◽

Vol 47 ◽

pp. 68-89 ◽

Cited By ~ 10

Author(s):

J. Brian Pitts

Keyword(s):

General Relativity ◽

Vector Field ◽

Killing Vector ◽

Killing Vector Field

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CCNV Space-Times as Potential Supergravity Solutions

Advances in Mathematical Physics ◽

10.1155/2018/5861481 ◽

2018 ◽

Vol 2018 ◽

pp. 1-7

Author(s):

A. Coley ◽

D. McNutt ◽

N. Pelavas

Keyword(s):

Vector Field ◽

Killing Vector ◽

Space Time ◽

Null Vector ◽

Killing Spinor ◽

Necessary Condition ◽

Killing Vector Field ◽

Higher Dimensional

It is of interest to study supergravity solutions preserving a nonminimal fraction of supersymmetries. A necessary condition for supersymmetry to be preserved is that the space-time admits a Killing spinor and hence a null or time-like Killing vector field. Any space-time admitting a covariantly constant null vector (CCNV) field belongs to the Kundt class of metrics and more importantly admits a null Killing vector field. We investigate the existence of additional non-space-like isometries in the class of higher-dimensional CCNV Kundt metrics in order to produce potential solutions that preserve some supersymmetries.

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