Ricci-Bourguignon solitons and Fischer-Marsden conjecture on generalized Sasakian-space-forms with $\beta$-Kenmotsu structure
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Our aim is to study the properties of Fischer-Marsden conjecture and Ricci-Bourguignon solitons within the framework of generalized Sasakian-space-forms with $\beta$-Kenmotsu structure. It is proven that a $(2n+1)$-dimensional generalized Sasakian-space-form with $\beta$-Kenmotsu structure satisfying the Fischer-Marsden equation is a conformal gradient soliton. Also, it is shown that a generalized Sasakian-space-form with $\beta$-Kenmotsu structure admitting a gradient Ricci-Bourguignon soliton is either $\Psi \backslash T^{k} \times M^{2n+1-k}$ or gradient $\eta$-Yamabe soliton.
Abstract
Our aim is to study the properties of Fischer-Marsden conjecture and Ricci-Bourguignon solitons within the framework of generalized Sasakian-space-forms with $\beta$-Kenmotsu structure. It is proven that a $(2n+1)$-dimensional generalized Sasakian-space-form with $\beta$-Kenmotsu structure satisfying the Fischer-Marsden equation is a conformal gradient soliton. Also, it is shown that a generalized Sasakian-space-form with $\beta$-Kenmotsu structure admitting a gradient Ricci-Bourguignon soliton is either $\Psi \backslash T^{k} \times M^{2n+1-k}$ or gradient $\eta$-Yamabe soliton.
참고문헌 (44)
- P. Alegre, "Generalized Sasakian-space-forms", Israel J. Math, 141, pp.157~183 (2004)[DOI]
- P. Alegre, "Structures on generalized Sasakian-space-forms", Differential Geom. Appl, 26(6), pp.656~666 (2008)[DOI]
- P. Alegre, "Generalized Sasakian space forms and conformal changes of the metric", Results Math, 59(3-4), pp.485~493 (2011)[DOI]
- P. Alegre, "New examples of generalized Sasakianspace-forms", Proc. Est. Acad. Sci, 60, pp.251~257 (2011)
- J. Berndt, "Real hypersurfaces with constant principal curvatures in complex space forms", Proceedings of the Tenth International Workshop on Differential Geometry, pp.1~12 (2006), Kyungpook Nat. Univ
- A. M. Blaga, "Harmonic forms and generalized solitons", ~ (2021)
- D. E. Blair, "Lecture Notes in Mathematics Vol. 509" (1976), Springer-Verlag
- D. E. Blair, "Contact manifolds with characteristic vector field annihilated by the curvature", Bull. Inst. Math. Acad. Sinica, 9(4), pp.533~545 (1981)
- W. M. Boothby, "On contact manifolds", Ann. of Math, 68(2), pp.721~734 (1958)[DOI]
- J. -P. Bourguignon, "Une stratification de l’espace des structures riemanniennes", Compos. Math, 30, pp.1~41 (1975)
- J.-P. Bourguignon, "Global differential geometry and global analysis (Berlin, 1979)", pp.42~63 (1981), Springer
- A. Carriazo, "Recent advances in the geometry of submanifolds—dedicated to the memory of Franki Dillen (1963–2013)", pp.17~25 (2016), Amer. Math. Soc
- A. Carriazo, "Generalized (κ, μ)-space forms", Mediterr. J. Math, 10(1), pp.475~496 (2013)[DOI]
- G. Catino, "The Ricci-Bourguignon flow", Pacific J. Math, 287(2), pp.337~370 (2017)[DOI]
- G. Catino, "On the global structure of conformal gradient solitons with nonnegative Ricci tensor", Commun. Contemp. Math, 14(6), pp.12~ (2012)[DOI]
- G. Catino, "Gradient Einstein solitons", Nonlinear Anal, 132, pp.66~94 (2016)[DOI]
- P. Cernea, "Killing fields generated by multiple solutions to the Fischer-Marsden equation", Internat. J. Math, 26(4), pp.18~ (2015)[DOI]
- S. K. Chaubey, "Characterization of perfect fluid spacetimes admitting gradient η-Ricci and gradient Einstein solitons", J. Geom. Phys, 162, pp.10~ (2021)[DOI]
- Sudhakar Kr Chaubey, "Kenmotsu manifolds satisfying the Fischer-Marsden equation", 대한수학회지, 58(3), pp.597~607 (2021), 대한수학회[DOI]
- S. K. Chaubey, "Invariant submanifolds of hyperbolic Sasakian manifolds and η-Ricci-Bourguignon solitons", Filomat, 36(2), pp.409~421 (2022)[DOI]
- S. K. Chaubey, "Almost η-Ricci-Bourguignon solitons on submersions from Riemannian submersions", Balkan J. Math. Appl, 27(1), pp.24~38 (2022)
- S. K. Chaubey, "W-semisymmetric generalized Sasakian-space-forms", Adv. Pure Appl. Math, 10(4), pp.427~436 (2019)[DOI]
- J. Corvino, "Scalar curvature deformation and a gluing construction for the Einstein constraint equations", Comm. Math. Phys, 214(1), pp.137~189 (2000)[DOI]
- U. C. De, "A note on almost co-K¨ahler manifolds", Int. J. Geom. Methods Mod. Phys, 17(10), pp.14~ (2020)[DOI]
- U. C. De, "Gradient Yamabe and gradient m-quasi Einstein metrics on three-dimensional cosymplectic manifolds", Mediterr. J. Math, 18(3), pp.14~ (2021)[DOI]
- S. Dwivedi, "Some results on Ricci-Bourguignon solitons and almost solitons", Canad. Math. Bull, 64(3), pp.591~604 (2021)[DOI]
- M. Falcitelli, "Locally conformal C6-manifolds and generalized Sasakian-space-forms", Mediterr. J. Math, 7(1), pp.19~36 (2010)[DOI]
- A. E. Fischer, "An introduction to conformal Ricci flow", Classical Quantum Gravity, 21(3), pp.S171~S218 (2004)[DOI]
- A. E. Fischer, "Manifolds of Riemannian metrics with prescribed scalar curvature", Bull. Amer. Math. Soc, 80, pp.479~484 (1974)[DOI]
- A. E. Fischer, "The structure of compact Ricci-flat Riemannian manifolds", J. Differential Geometry, 10, pp.277~288 (1975)
- R. S. Hamilton, "Three-manifolds with positive Ricci curvature", J. Differential Geometry, 17(2), pp.255~306 (1982)[DOI]
- P. T. Ho, "On the Ricci-Bourguignon flow", Internat. J. Math, 31(6), pp.40~ (2020)[DOI]
- M. Kanai, "On a differential equation characterizing a Riemannian structure of a manifold", Tokyo J. Math, 6(1), pp.143~151 (1983)[DOI]
- U.-H. Ki, "On real hypersurfaces of a complex space form", Math. J. Okayama Univ, 32, pp.207~221 (1990)
- U. K. Kim, "Conformally flat generalized Sasakian-space-forms and locally symmetric generalized Sasakian-space-forms", Note Mat, 26(1), pp.55~67 (2006)
- O. Kobayashi, "A differential equation arising from scalar curvature function", J. Math. Soc. Japan, 34(4), pp.665~675 (1982)[DOI]
- J. Lafontaine, "Sur la g´eom´etrie d’une g´en´eralisation de l’´equation diff´erentielle d’Obata", J. Math. Pures Appl, 62(1), pp.63~72 (1983)
- M. Obata, "Certain conditions for a Riemannian manifold to be isometric with a sphere", J. Math. Soc. Japan, 14, pp.333~340 (1962)[DOI]
- D. S. Patra, "The Fischer-Marsden conjecture and contact geometry", Period. Math. Hungar, 76(2), pp.207~216 (2018)[DOI]
- D. G. Prakasha, "The Fischer-Marsden conjecture on non-Kenmotsu (κ, μ)′-almost Kenmotsu manifolds", J. Geom, 110(1), pp.9~ (2019)[DOI]
- S. Sasaki, "On differentiable manifolds with certain structures which are closely related to almost contact structure I", Tohoku Math. J, 12(2), pp.459~476 (1960)[DOI]
- Y. Shen, "A note on Fischer-Marsden’s conjecture", Proc. Amer. Math. Soc, 125(3), pp.901~905 (1997)[DOI]
- Y. J. Suh, "On real hypersurfaces of a complex space form with η-parallel Ricci tensor", Tsukuba J. Math, 14(1), pp.27~37 (1990)[DOI]
- S. Sular, "Contact CR-warped product submanifolds in generalized Sasakian space forms", Turkish J. Math, 36(3), pp.485~497 (2012)[DOI]
