REMARKS ON SUBMANIFOLDS AS ALMOST eta-RICCI-BOURGUIGNON SOLITONS
Abstract
We give some characterizations for submanifolds admitting almost $\eta$-Ricci-Bourguignon solitons whose potential vector field is the tangential component of a concurrent vector field on the ambient manifold. We describe the particular cases of umbilical submanifolds and of hypersurfaces in a space with constant curvature.
Keywords
Full Text:
PDFReferences
bibitem{adaracihan} Blaga, A. M., "{O}zg"{u}r, C.: {Almost $eta $-Ricci and almost $eta $-Yamabe solitons with torse-forming potential vector field}. Quaestiones Mathematicae textbf{45}(1), (2022), 143--163.
bibitem{catmazz} Catino, G., Mazzieri, L.: Gradient Einstein solitons. J. Nonlin. Anal. textbf{132} (2016), 66--94.
bibitem{CM-00} Chaki, M. C.; Maity, R. K.: On quasi Einstein manifolds. Publ. Math. Debrecen textbf{57}(3-4) (2000), 297--306.
bibitem{Chen-16} Chen, B.-Y.: A survey on Ricci solitons on Riemannian submanifolds, Recent advances in the geometry of submanifolds -- dedicated to the memory of Franki Dillen (1963--2013), 27--39, Contemp. Math. textbf{674}, Amer. Math. Soc., Providence, RI, 2016.
bibitem{Deszcz} Deszcz R.: On pseudo-symmetric spaces. Bull. Soc. Math. Belgium S'{e}rie A textbf{44} (1992), 1--34.
bibitem{DVY} Deszcz R., Verstraelen L., Yaprak c{S}.: Pseudosymmetric hypersurfaces in $4$-dimensional spaces of constant curvature. Bull. Inst. Math. Acad. Sinica textbf{22} (1994), 167--179.
bibitem{ham} Hamilton, R. S.: The Ricci flow on surfaces. Math. and general relativity (Santa Cruz, CA, 1986). Contemp. Math. textbf{71} (1988),
--262.
bibitem{siak} Siddiqi, M. D., Akyol, M. A.: $eta$-Ricci-Yamabe Soliton on Riemannian Submersions from Riemannian manifolds, arXiv:2004.14124v1.2020.
bibitem{h} {Al-Sodais, H., Alodan, H., Deshmukh, S.}: Hypersurfaces of Euclidean space as gradient Ricci solitons. An. c{S}t. Univ. Al. I. Cuza, Iac{s}i (S. N.), Matematicu{a} textbf{LXI}, f.2 (2015), 437--444.
bibitem{Yano43} Yano, K.: Sur le parall'{e}lisme et la concourance dans l'espace de Riemann. Proc. Imp. Acad. Tokyo textbf{19} (1943), 189--197.
DOI: https://doi.org/10.22190/FUMI220318027B
Refbacks
- There are currently no refbacks.
ISSN 0352-9665 (Print)