On Multiply Warped Product Gradient Ricci Soliton

Автор(и)

  • Tamalika Dutta Department of Mathematics, Raja Rammohun Roy Mahavidyalaya Radhanagar-712406, India
  • Sampa Pahan Department of Mathematics, Mrinalini Datta Mahavidyapith, Kolkata-700051, India
  • X. Chen College of Science, China University, Beijing-102249, China
  • Arindam Bhattacharyya Department of Mathematics, Jadavpur University, Kolkata-700032, India

DOI:

https://doi.org/10.15407/mag19.03.603

Анотація

Метою роботи є вивчення градiєнтного солiтону Рiччi, що є множинно викривленим добутком. Ми доводимо, що коли многовид є повним, то тодi потенцiальна функцiя залежить лише вiд бази, а шар повинен бути енштейновим многовидом. Також ми наводимо необхiднi та достатнi умови для побудови градiєнтного солiтону Рiччi, що є множинно викривленим добутком.

Mathematical Subject Classification 2020: 53C24, 53C25, 53C21

Ключові слова:

солiтон Рiччi, викривлений добуток, множинно викривлений добуток

Посилання

C. Wolf, A mathematical model for the propagation of a hantavirus in structured populations, Discrete Contin. Dyn. Syst. Ser. B 4 (2004), 1065--1089. https://doi.org/10.3934/dcdsb.2004.4.1065

R.L. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969), 1--49. https://doi.org/10.1090/S0002-9947-1969-0251664-4

V. Borges and K. Tenenblat, Ricci almost solitons on semi-Riemannian warped products, Mathematische Nachrichten (2022), 295, 1--22. https://doi.org/10.1002/mana.201900242

X. Cao, Compact gradient shrinking Ricci solitons with positive curvature operator, J. Geom. Anal. 17 (2007), 425--433. https://doi.org/10.1007/BF02922090

J. Choi, Multiply warped products with nonsmooth metrics, J. Math. Phys. 41, (2000), 8163--8169. https://doi.org/10.1063/1.1287432

B. Chow, S.C. Chu, D. Glickenstein, C. Guenther, J. Isenberg, T. Ivey, D. Knopf, P. Lu, F. Luo, and L. Ni, The Ricci Flow: Techniques and Applications Part I: Geometric Aspects. Mathematical surveys and Monographs, Amer. Math. Soc., Providence, RI, 2007. https://doi.org/10.1090/surv/144

F. Dobarro and B. Ünal, Curvature of multiply warped products, J. Geom. Phys. 55 (2005), 75--106. https://doi.org/10.1016/j.geomphys.2004.12.001

D. Dumitru, Special multiply Einstein warped products with an affine connection, Int. J. Geom. Meth. Modern Phys. 15 (2018), 1850107. https://doi.org/10.1142/S0219887818501074

F.E.S. Feitosa, A.A. Freitas Filho, and J.N.V. Gomes, On the construction of gradient Ricci soliton warped product, Nonlinear Anal. 161 (2017), 30--43. https://doi.org/10.1016/j.na.2017.05.013

R.S. Hamilton, Three manifold with positive Ricci curvature, J. Differential Geom. 17 (1982), 255--306. https://doi.org/10.4310/jdg/1214436922

R.S. Hamilton, The formation of singularities in the Ricci flow, Surveys in Differential Geometry(Cambridge, MA, 1993), International Press, Cambridge, MA, 2 (1995), 7--136. https://doi.org/10.4310/SDG.1993.v2.n1.a2

T. Ivey, New examples of complete Ricci solitons, Proc. Amer. Math. Soc. 122 (1994), 241--245. https://doi.org/10.1090/S0002-9939-1994-1207538-5

B.H. Kim, S.D. Lee, J.H. Choi, and Y.O. Lee, On warped product spaces with a certain Ricci condition, Bull. Korean Math. Soc. 50, (2013), 1683--1691. https://doi.org/10.4134/BKMS.2013.50.5.1683

B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York (1983).

S. Pahan, B. Pal, and A. Bhattacharyya, On Einstein warped products with a quarter-symmetric connection, Int. J. Geom. Meth. Modern Phys. 14, (2017), 1750050. https://doi.org/10.1142/S0219887817500505

R.S. Pina and M.L. Sousa, Gradient Ricci solitons with structure of warped product, Results. Math. 71 (2017), 825--840. https://doi.org/10.1007/s00025-016-0583-2

B. Ünal, Doubly Warped Products, Ph. D. Thesis, University of Missouri-Columbia, 2000.

B. Ünal, Multiply Warped Products, J. Geom. Phys. 34 (2000), 287--301. https://doi.org/10.1016/S0393-0440(99)00072-8

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Dutta, T.; Pahan, S.; Chen, X.; Bhattacharyya, A. On Multiply Warped Product Gradient Ricci Soliton. Журн. мат. фіз. анал. геом. 2023, 19, 603-615.

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