Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ANTI-INVARIANT SUBMERSIONS FROM ALMOST PARACONTACT RIEMANNIAN MANIFOLDS

  • Received : 2019.03.04
  • Accepted : 2019.04.19
  • Published : 2019.12.25
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Abstract

We introduce anti-invariant Riemannian submersions from almost paracontact Riemannian manifolds onto Riemannian manifolds. We give an example, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and check the harmonicity of such submersions.

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References

  1. Akyol, M. A. and B. Sahin, Conformal anti-invariant submersions from almost Hermitian manifolds, Turkish Journal of Mathematics, 40(1)(2016): 43-70 https://doi.org/10.3906/mat-1408-20
  2. Baird, P. and Wood, J.C., Harmonic morphisms between Riemannian manifolds. Oxford science publications, 2003.
  3. Bourguignon, J.P. and Lawson, H.B., A mathematician's visit to Kaluza- Klein theory, Rend. Sem. Mat. Univ. Politec. Torino, Special Issue, (1989) 143-163.
  4. Bourguignon, J.P. and Lawson, H.B., Stability and isolation phenomena for Yang-Mills fields, Comm. Math. Phys. 79, (1981) 189-230. https://doi.org/10.1007/BF01942061
  5. Cayir, H., Lie derivatives of almost contact structure and almost paracontact structure with respect to $X^V$ and $X^H$ on tangent bundle T(M) , Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, 42(1)(2016): 38-49.
  6. Cayir, H. and Akdag, K., Some notes on almost paracomplex structures associated with the diagonal lifts and operators on cotangent bundle, New Trends in Math. Sciences, 4(4)(2016): 42-50 https://doi.org/10.20852/ntmsci.2016422036
  7. Cayir, H. and Koseoglu, G., Lie derivatives of almost contact structure and almost paracontact structure with respect to $X^C$ and $X^V$ on tangent bundle T(M), New Trends in Mathematical Sciences. 4(1)(2016): 153-159. https://doi.org/10.20852/ntmsci.2016115657
  8. J. Eells, J.H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964), 109-160. https://doi.org/10.2307/2373037
  9. Falcitelli, M., Ianus, S. and Pastore, A.M., Riemannian submersions and related topics, World Scientific, 2004.
  10. Gray, A., Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech. 16,(1967) 715-737.
  11. Gunduzalp, Y., Slant submersions from almost paracontact Riemannian manifolds, Kuwait Journal of Sci., 42(1), (2015), 17-29.
  12. Gunduzalp, Y. and Sahin, B., Paracontact semi-Riemannian submersions, Turkish Journal of Mathematics, 37(1),(2013) 114-128.
  13. Gunduzalp, Y. and Akyol, M.A., Conformal slant submersions from cosymplectic manifolds, Turkish Journal of Mathematics, 42,(2018) 2672-2689. https://doi.org/10.3906/mat-1803-106
  14. Ianus, S., Mazzocco, R. and Vilcu, G. E, Riemannian submersions from quaternionic manifolds, Acta Appl. Math. 104, (2008) 83-89. https://doi.org/10.1007/s10440-008-9241-3
  15. Ianus, S. and Visinescu, M., Kaluza-Klein theory with scalar fields and generalised Hopf manifolds, Classical Quantum Gravity 4, (1987) 1317-1325. https://doi.org/10.1088/0264-9381/4/5/026
  16. Ianus, S. and Visinescu, M., Space-time compactification and Riemannian submersions, The mathematical heritage of C.F. Gauss, World Sci. Publ., River Edge, NJ, (1991) 358-371.
  17. Ianus, S., Matsumoto, K. and Mihai, I., Almost semi-invariant submanifolds of some almost paracontact Riemannian manifolds, Bulletin of Yamagata University, 11(2), (1985) 121-128.
  18. Mustafa, M.T., Applications of harmonic morphisms to gravity. J. Math. phys. 41, (2000) 6918-6929. https://doi.org/10.1063/1.1290381
  19. O'Neill, B., The fundamental equations of a submersion, Michigan Math. J. 13, (1996) 459-469.
  20. Park, K.S., H-slant submersions. Bull. Korean Math. Soc. 49, 329-338(2012). https://doi.org/10.4134/BKMS.2012.49.2.329
  21. Sahin, B., Slant submersions from almost Hermitian manifolds, Bull. Math. Soc.Sci. Math. Roumanie Tome 54(102), (2011) 93-105.
  22. Sahin, B., Anti-invariant Riemannian submersions from almost Hermitian manifolds, Cent. Eur. J. Math. 8(3), (2010) 437-447. https://doi.org/10.2478/s11533-010-0023-6
  23. Watson, B., Almost Hermitian submersions. J. Diff. Geom. 11, (1976) 147-165. https://doi.org/10.4310/jdg/1214433303
  24. Watson, B., G,G'-Riemannian submersions and nonlinear gauge field equations of general relativity, Global analysis on manifolds Teubner-Texte Math.,57,Teubner, Leipzig, (1983) 324-249.