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TMF, 2003, Volume 134, Number 3, Pages 382–387 (Mi tmf170)  

This article is cited in 16 scientific papers (total in 16 papers)

The Killing–Yano Tensor

S. E. Stepanov

Vladimir State Pedagogical University

Abstract: We obtain a general solution of the equations determining the Killing–Yano tensor of rank $p$ on an $n$-dimensional $(1\leqslant p\leqslant n-1)$ pseudo-Riemannian manifold of constant curvature and discuss possible applications of the obtained result.

Keywords: constant curvature manifold, Killing–Yano tensor, Maxwell equations, Dirac equations

DOI: https://doi.org/10.4213/tmf170

Full text: PDF file (195 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2003, 134:3, 333–338

Bibliographic databases:

Received: 27.02.2002
Revised: 03.04.2002

Citation: S. E. Stepanov, “The Killing–Yano Tensor”, TMF, 134:3 (2003), 382–387; Theoret. and Math. Phys., 134:3 (2003), 333–338

Citation in format AMSBIB
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\issue 3
\pages 333--338
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. E. Stepanov, M. V. Smolnikova, “Affine differential geometry of Killing tensors”, Russian Math. (Iz. VUZ), 48:11 (2004), 74–78  mathnet  mathscinet
    2. Cariglia, M, “Quantum mechanics of Yano tensors: Dirac equation in curved spacetime”, Classical and Quantum Gravity, 21:4 (2004), 1051  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. S. E. Stepanov, “Vanishing theorems in affine, Riemannian, and Lorenz geometries”, J. Math. Sci., 141:1 (2007), 929–964  mathnet  crossref  mathscinet  zmath  elib
    4. S. E. Stepanov, “Some conformal and projective scalar invariants of Riemannian manifolds”, Math. Notes, 80:6 (2006), 848–852  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. S. E. Stepanov, “Curvature and Tachibana numbers”, J. Math. Sci., 172:6 (2011), 901–908  mathnet  crossref  mathscinet
    6. Acik O., Ertem U., Onder M., Vercin A., “Killing-Yano forms of a class of spherically symmetric space-times: A unified generation of higher forms”, Journal of Mathematical Physics, 51:2 (2010), 022502  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    7. S. E. Stepanov, “Curvature and Tachibana numbers”, Sb. Math., 202:7 (2011), 1059–1069  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. Santillan O.P., “Hidden Symmetries and Supergravity Solutions”, J. Math. Phys., 53:4 (2012), 043509  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    9. Mikes J., Stepanov S., Hinterleitner I., “Projective Mappings and Dimensions of Vector Spaces of Three Types of Killing-Yano Tensors on Pseudo Riemannian Manifolds of Constant Curvature”, XX International Fall Workshop on Geometry and Physics, AIP Conference Proceedings, 1460, eds. Linan M., Barbero F., DeDiego D., Amer Inst Physics, 2012, 202–205  crossref  adsnasa  isi
    10. Stepanov S.E., Mikes J., “Betti and Tachibana Numbers of Compact Riemannian Manifolds”, Differ. Geom. Appl., 31:4 (2013), 486–495  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    11. Stepanov S.E., Mikes J., “Betti and Tachibana Numbers”, Miskolc Math. Notes, 14:2 (2013), 475–486  mathscinet  zmath  isi
    12. Stepanov S.E., Jukl M., Mikes J., “On Dimensions of Vector Spaces of Conformal Killing Forms”, Algebra, Geometry and Mathematical Physics (Agmp), Springer Proceedings in Mathematics & Statistics, 85, eds. Makhlouf A., Paal E., Silvestrov S., Stolin A., Springer, 2014, 495–507  crossref  mathscinet  zmath  isi  scopus  scopus
    13. Stepanov S.E., Jukl M., Mikes J., “Vanishing Theorems of Conformal Killing Forms and Their Applications To Electrodynamics in the General Relativity Theory”, Int. J. Geom. Methods Mod. Phys., 11:9 (2014), 1450039  crossref  mathscinet  zmath  isi  scopus  scopus
    14. Mikes J. Stepanova E. Vanzurova A., “Differential Geometry of Special Mappings”, Differential Geometry of Special Mappings, Palacky Univ, 2015, 1–566  mathscinet  isi
    15. Khavkine I., “Cohomology with Causally Restricted Supports”, Ann. Henri Poincare, 17:12 (2016), 3577–3603  crossref  mathscinet  zmath  isi  scopus
    16. Khavkine I., “The Calabi complex and Killing sheaf cohomology”, J. Geom. Phys., 113 (2017), 131–169  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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