대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제37권4호
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  • Pages.1199-1207
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  • 2022
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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RIEMANNIAN SUBMERSIONS WHOSE TOTAL SPACE IS ENDOWED WITH A TORSE-FORMING VECTOR FIELD

  • 투고 : 2021.10.13
  • 심사 : 2021.12.30
  • 발행 : 2022.10.01
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초록

In the present paper, a Riemannian submersion 𝜋 between Riemannian manifolds such that the total space of 𝜋 endowed with a torse-forming vector field 𝜈 is studied. Some remarkable results of such a submersion whose total space is Ricci soliton are given. Moreover, some characterizations about any fiber of 𝜋 or the base manifold B to be an almost quasi-Einstein are obtained.

키워드

과제정보

This work is supported by 1001-Scientific and Technological Research Projects Funding Program of TUBITAK project number 117F434.

참고문헌

  1. C. Altafini, Redundant robotic chains on Riemannian submersions, IEEE Trans. Rob. Aut. 20 (2004), 335-340.
  2. B.-Y. Chen, Some results on concircular vector fields and their applications to Ricci solitons, Bull. Korean Math. Soc. 52 (2015), no. 5, 1535-1547. https://doi.org/10.4134/BKMS.2015.52.5.1535
  3. B.-Y. Chen, Concircular vector fields and pseudo-Kaehler manifolds, Kragujevac J. Math. 40 (2016), no. 1, 7-14. https://doi.org/10.5937/KgJMath1601007C
  4. B.-Y. Chen, Classification of torqued vector fields and its applications to Ricci solitons, Kragujevac J. Math. 41 (2017), no. 2, 239-250. https://doi.org/10.5937/kgjmath1702239c
  5. M. Falcitelli, S. Ianus, and A. M. Pastore, Riemannian Submersions and Related Topics, World Scientific Publishing Co., Inc., River Edge, NJ, 2004. https://doi.org/10.1142/9789812562333
  6. A. Gray, Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech. 16 (1967), 715-737.
  7. R. S. Hamilton, The Ricci flow on surfaces, in Mathematics and general relativity (Santa Cruz, CA, 1986), 237-262, Contemp. Math., 71, Amer. Math. Soc., Providence, RI, 1988. https://doi.org/10.1090/conm/071/954419
  8. E. Meri,c and E. Kili,c, Riemannian submersions whose total manifolds admit a Ricci soliton, Int. J. Geom. Methods Mod. Phys. 16 (2019), no. 12, 1950196, 12 pp. https://doi.org/10.1142/S0219887819501962
  9. B. O'Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 459-469. http://projecteuclid.org/euclid.mmj/1028999604
  10. C. Ozgur, On some classes of super quasi-Einstein manifolds, Chaos, Solitons & Fractals 40 (2009), 1156-1161.
  11. G. Perelman, The Entropy formula for the Ricci flow and its geometric applications, arXiv math/0211159, (2002).
  12. S. Pigola, M. Rigoli, M. Rimoldi, and A. G. Setti, Ricci almost solitons, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 10 (2011), no. 4, 757-799.