Ir al contenido

Documat


Ricci–Bourguignon solitons on real hypersurfaces in the complex projective space

  • Imsoon Jeong [1] ; Young Jin Suh [2]
    1. [1] Cheongju University

      Cheongju University

      Corea del Sur

    2. [2] Kyungpook National University

      Kyungpook National University

      Corea del Sur

  • Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 68, Nº. 1, 2025, págs. 277-295
  • Idioma: inglés
  • DOI: 10.33044/revuma.3849
  • Enlaces
  • Resumen
    • We give a complete classification of Ricci–Bourguignon solitons on real hypersurfaces in the complex projective space CP n = SUn+1/S(U1 · Un). Next, as an application, we give some non-existence properties for gradient Ricci–Bourguignon solitons on real hypersurfaces with isometric Reeb flow and contact real hypersurfaces in the complex projective space CP n.

  • Referencias bibliográficas
    • J. Berndt and Y. J. Suh, Real hypersurfaces in Hermitian symmetric spaces, Advances in Analysis and Geometry 5, De Gruyter, Berlin, 2022....
    • A. M. Blaga and H. M. Tas¸tan, Some results on almost η-Ricci–Bourguignon solitons, J. Geom. Phys. 168 (2021), article no. 104316. DOI MR...
    • D. E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Math. 509, Springer, Berlin-New York, 1976. MR Zbl
    • J.-P. Bourguignon, Une stratification de l’espace des structures riemanniennes, Compositio Math. 30 (1975), 1–41. MR Zbl
    • J.-P. Bourguignon, Ricci curvature and Einstein metrics, in Global differential geometry and global analysis (Berlin, 1979), Lecture Notes...
    • G. Catino, L. Cremaschi, Z. Djadli, C. Mantegazza, and L. Mazzieri, The Ricci–Bourguignon flow, Pacific J. Math. 287 no. 2 (2017), 337–370....
    • G. Catino and L. Mazzieri, Gradient Einstein solitons, Nonlinear Anal. 132 (2016), 66–94. DOI MR Zbl
    • G. Catino, L. Mazzieri, and S. Mongodi, Rigidity of gradient Einstein shrinkers, Commun. Contemp. Math. 17 no. 6 (2015), article no. 1550046....
    • T. E. Cecil and P. J. Ryan, Focal sets and real hypersurfaces in complex projective space, Trans. Amer. Math. Soc. 269 no. 2 (1982), 481–499....
    • P. Cernea and D. Guan, Killing fields generated by multiple solutions to the Fischer–Marsden equation, Internat. J. Math. 26 no. 4 (2015),...
    • S. K. Chaubey, U. C. De, and Y. J. Suh, Kenmotsu manifolds satisfying the Fischer–Marsden equation, J. Korean Math. Soc. 58 no. 3 (2021),...
    • S. K. Chaubey, Y. J. Suh, and U. C. De, Characterizations of the Lorentzian manifolds admitting a type of semi-symmetric metric connection,...
    • U. C. De, S. K. Chaubey, and Y. J. Suh, Gradient Yamabe and gradient m-quasi Einstein metrics on three-dimensional cosymplectic manifolds,...
    • M. Djoric´ and M. Okumura, CR submanifolds of complex projective space, Developments in Mathematics 19, Springer, New York, 2010. DOI MR Zbl
    • S. Dwivedi, Some results on Ricci–Bourguignon solitons and almost solitons, Canad. Math. Bull. 64 no. 3 (2021), 591–604. DOI MR Zbl
    • R. S. Hamilton, The Ricci flow on surfaces, in Mathematics and general relativity (Santa Cruz, CA, 1986), Contemp. Math. 71, American Mathematical...
    • S. Helgason, Differential geometry, Lie groups, and symmetric spaces, Graduate Studies in Mathematics 34, American Mathematical Society, Providence,...
    • I. Jeong and Y. J. Suh, Pseudo anti-commuting and Ricci soliton real hypersurfaces in complex two-plane Grassmannians, J. Geom. Phys. 86 (2014),...
    • U.-H. Ki and Y. J. Suh, On real hypersurfaces of a complex space form, Math. J. Okayama Univ. 32 (1990), 207–221. MR Zbl
    • S. Kobayashi and K. Nomizu, Foundations of differential geometry. Vol. II, Wiley Classics Library, John Wiley & Sons, New York, 1996....
    • J. Morgan and G. Tian, Ricci flow and the Poincar´e conjecture, Clay Mathematics Monographs 3, American Mathematical Society, Providence,...
    • M. Okumura, On some real hypersurfaces of a complex projective space, Trans. Amer. Math. Soc. 212 (1975), 355–364. DOI MR Zbl
    • B. O’Neill, Semi-Riemannian geometry, Pure and Applied Mathematics 103, Academic Press, New York, 1983. MR Zbl
    • G. Perelman, Ricci flow with surgery on three-manifolds, 2003. arXiv:math/0303109 [math.DG].
    • J. D. Perez ´ , Commutativity of Cho and structure Jacobi operators of a real hypersurface in a complex projective space, Ann. Mat. Pura Appl....
    • A. Romero, On a certain class of complex Einstein hypersurfaces in indefinite complex space forms, Math. Z. 192 no. 4 (1986), 627–635. DOI...
    • A. Romero, Some examples of indefinite complete complex Einstein hypersurfaces not locally symmetric, Proc. Amer. Math. Soc. 98 no. 2 (1986),...
    • B. Smyth, Differential geometry of complex hypersurfaces, Ann. of Math. (2) 85 (1967), 246–266. DOI MR Zbl
    • Y. J. Suh, Real hypersurfaces of type B in complex two-plane Grassmannians, Monatsh. Math. 147 no. 4 (2006), 337–355. DOI MR Zbl
    • Y. J. Suh, Hypersurfaces with isometric Reeb flow in complex hyperbolic two-plane Grassmannians, Adv. in Appl. Math. 50 no. 4 (2013), 645–659....
    • Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians with harmonic curvature, J. Math. Pures Appl. (9) 100 no. 1 (2013), 16–33....
    • R. Takagi, On homogeneous real hypersurfaces in a complex projective space, Osaka J. Math. 10 (1973), 495–506. MR Zbl Available at http://projecteuclid.org/euclid.ojm/1200694557.
    • Y. Wang, Ricci solitons on almost Kenmotsu 3-manifolds, Open Math. 15 no. 1 (2017), 1236–1243. DOI MR Zbl
    • Y. Wang, Ricci solitons on almost co-K¨ahler manifolds, Canad. Math. Bull. 62 no. 4 (2019), 912–922. DOI MR Zbl
    • K. Yano and M. Kon, CR submanifolds of Kaehlerian and Sasakian manifolds, Progress in Mathematics 30, Birkh¨auser, Boston, MA, 1983. MR Zbl

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno