Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

ALMOST HERMITIAN SUBMERSIONS WHOSE TOTAL MANIFOLDS ADMIT A RICCI SOLITON

  • Received : 2020.05.05
  • Accepted : 2020.08.21
  • Published : 2020.12.25
Download PDF
⟨ Previous Next ⟩

Abstract

The object of the present paper is to study the almost Hermitian submersion from an almost Hermitian manifold admits a Ricci soliton. Where, we investigate any fibre of such a submersion is a Ricci soliton or Einstein. We also get necessary conditions for which the base manifold of an almost Hermitian submersion is a Ricci soliton or Einstein. Moreover, we obtain the harmonicity of an almost Hermitian submersion from a Ricci soliton to an almost Hermitian manifold.

Keywords

References

  1. M. A. Akyol and S. Beyendi, Riemannian submersions endowed with a semi-symmetric non-metric connection, Konuralp Journal of Mathematics, 6(1) (2018) 188-193.
  2. A. M. Blaga, S. Y. Perktas, B. E. Acet and F. E. Erdogan, η-Ricci solitons in (ε)- paracontact metric manifolds, Glasnik Matematicki, 53(73) (2018), 205-220. https://doi.org/10.3336/gm.53.1.14
  3. G.Calvaruso and A. Perrone, Ricci solitons in three-dimensional paracontact geometry, Journal of Geometry and Physics, 98 (2015), 1-12. https://doi.org/10.1016/j.geomphys.2015.07.021
  4. H. D. Cao, Geometry of Ricci solitons, Chin. Ann. Math. Ser. B 27 (2006), 141-162.
  5. B.-Y. Chen and S. Deshmukh, Geometry of compact shrinking Ricci solitons, Balkan J. Geom. Appl. 19 (2014), 13-21.
  6. B.-Y. Chen, Concircular vector fields and Pseudo-Kaehler manifolds, Kragujevac Journal of Mathematics 40 (2016), 7-14. https://doi.org/10.5937/KgJMath1601007C
  7. D. Chinea, Almost contact metric submersions, Rend. Circ. Mat. Palermo, II Ser. 34, 89-104, 1985. https://doi.org/10.1007/BF02844887
  8. J. T. Cho and M. Kimura Ricci solitons and real hypersurfaces in a complex space form, Tohoku Math. J. 61 (2009) 205-212. https://doi.org/10.2748/tmj/1245849443
  9. A. Ghosh and R. Sharma, K-contact metrics as a Ricci soliton, Beitr. Algebra Geom., 53 (2012), 25-30. https://doi.org/10.1007/s13366-011-0038-6
  10. J. Eells, J.H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964), 109-160. https://doi.org/10.2307/2373037
  11. M. Falcitelli, S. Ianus and A. M. Pastore, Riemannian Submersions and Related Topics, World Scientific, 2004.
  12. M. Falcitelli, A note on almost Kahler and nearly Kahler submersions, J. Geom., 69 (2000), 79-87. https://doi.org/10.1007/BF01237477
  13. A. Gray, Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech. 16 (1967), 715-737.
  14. Y. Gunduzalp and B. Sahin, Paracontact semi-Riemannian submersions, Turkish J. Math., 37,(2013), 114-128.
  15. Y. Gunduzalp and B. Sahin, Para-Contact Para-Complex Semi-Riemannian Submersions, Bull. Malays. Math. Sci. Soc 37(1) (2014), 139-152.
  16. Y. Gunduzalp and M. A. Akyol, Conformal slant submersions from cosymplectic manifolds, Turkish Journal of Mathematics 42(5) (2018), 2672-2689. https://doi.org/10.3906/mat-1803-106
  17. R. S. Hamilton, The Ricci flow on surfaces, Contemp. Math. 71 (1988) 237-261. https://doi.org/10.1090/conm/071/954419
  18. D. L. Johnson, Kahler submersions and holomorphic connections, J. Differential Geometry, 15 (1980), 71-79. https://doi.org/10.4310/jdg/1214435384
  19. S. Ianus, A. M. Ionescu, R. Mocanu, and G. E. Vilcu, Riemannian submersions from almost contact metric Manifols, Abh. Math. Semin. Univ. Hamburg 81(1)(2011) 101-114. https://doi.org/10.1007/s12188-011-0049-0
  20. S. Ianus, R. Mazzocco and G. E. Vilcu, Riemannian submersions from quaternionic manifolds, Acta Appl. Math. 104 (2008), 83-89. https://doi.org/10.1007/s10440-008-9241-3
  21. S. E. Meric and E. Kilic, Riemannian submersions whose total manifolds admit a Ricci soliton, Int J Geom Methods Mod Phys, 16(12) (2019), 1950196. https://doi.org/10.1142/s0219887819501962
  22. B. O'Neill, The fundamental equations of a submersion, Michigan Math. J. 13, 459-469, 1966. https://doi.org/10.1307/mmj/1028999604
  23. S. Pigola, M. Rigoli, M. Rimoldi and A.G. Setti, Ricci almost solitons, Ann. Scuola Norm Sup. Pisa. CI. Sci., 10(4), 757-799, 2011.
  24. D. S. Patra, Ricci solitons and Ricci almost solitons on para-Kenmotsu manifold, Bull. Korean Math. Soc. 56,5, (2019), 1315-1325. https://doi.org/10.4134/bkms.b181175
  25. B. Sahin, Riemannian submersions, Riemannian maps in Hermitian Geometry, and their Applications, Elsevir, Academic, Amsterdam, (2017).
  26. B. Watson, Almost Hermitian submersions, J. Differential Geom. 11, (1976) 147-165. https://doi.org/10.4310/jdg/1214433303
  27. K. Yano and M. Kon, Structures on Manifolds, Singapore: World Scientific, 1984.