ON RICCI SOLITONS AND SUBMANIFOLDS WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

Yusuf Doğru

DOI Number
https://doi.org/10.22190/FUMI240402028D
First page
375
Last page
385

Abstract


We consider Ricci solitons with a semi-symmetric non-metric connection. We find some properties, when the potential vector field is torse-forming. Applications to submanifolds are also given.

Keywords

Ricci soliton, semi-symmetric non-metric connection, torse-forming vector field, quasi-Einstein manifold, hyper-generalized quasi-Einstein manifold.

Full Text:

PDF

References


N. S. Agashe and M. R. Chafle: A semi-symmetric non-metric connection on a Riemannian manifold. Indian J. Pure Appl. Math. 23(6)(1992), 399–409.

N. S. Ageshe and M. R. Chafle: On submanifolds of a Riemannian manifold with a SSNMC. Tensor (N.S.) 55(2) (1994), 120–130.

H. Al-Sodais, H. Alodan and S. Deshmukh: Hypersurfaces of Euclidean space as gradient Ricci solitons. An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 61 (2015), 437–444.

A. L. Besse: Einstein manifolds. Classics in Mathematics, Springer-Verlag, Berlin (2008).

A. M. Blaga and C. Ozgur: Almost η-Ricci and almost η-Yamabe solitons with torse-forming potential vector field. Quaest. Math. 45 (2022), 143–163.

M. C. Chaki: On generalized quasi Einstein manifolds. Publ. Math. Debrecen 58 (2001), 683–691.

M. C. Chaki and R. K. Maity: On quasi Einstein manifolds. Publ. Math. Debrecen 57 (2000), 297–306.

B. Y. Chen: A survey on Ricci solitons on Riemannian submanifolds. Recent advances in the geometry of submanifolds-dedicated to the memory of Franki Dillen (1963–2013), Contemp. Math. 674 (2016), 27–39, Amer. Math. Soc., Providence, RI.

B. Y. Chen: Classification of torqued vector fields and its applications to Ricci solitons. Kragujevac J. Math. 41 (2017), 239–250.

Y. Dogru: η-Ricci-Bourguignon solitons with a semi-symmetric metric and semisymmetric non-metric connection. AIMS Math. 8(5) (2023), 11943–11952.

A. Fialkow: Conformal geodesics. Trans. Amer. Math. Soc. 45 (1939), 443–473.

A. Friedmann and J. A. Schouten: Uber die Geometrie der halbsymmetrischen Ubertragungen. Math. Z. 21 (1924), 211–223.

R. S. Hamilton: The Ricci flow on surfaces. Mathematics and general relativity (Santa Cruz, CA, 1986), 237–262, Contemp. Math. 71 (1988), Amer. Math. Soc., Providence, RI.

R. S. Hamilton: Three-manifolds with positive Ricci curvature. J. Differential Geometry 17 (1982), 255–306.

J. Inoguchi: Minimal surfaces in 3-dimensional solvable Lie groups. Chinese Ann. Math. Ser. B 24 (2003), 73–84.

A. Mihai and I. Mihai: Torse forming vector fields and exterior concurrent vector fields on Riemannian manifolds and applications. J. Geom. Phys. 73 (2013), 200–208.

C. OzgUr: On Ricci solitons with a semi-symmetric metric connection. Filomat 35(11) (2021), 3635–3641.

J. A. Schouten: Ricci-Calculus: An introduction to tensor analysis and its geometrical applications, 2nd. ed. Die Grundlehren der mathematischen Wissenschaften, Springer-Verlag, Berlin-G¨ottingen-Heidelberg (1954).

A. A. Shaikh, C. Ozgur and A. Patra: On hyper-generalized quasi-Einstein manifolds. Int. J. Math. Sci. Eng. Appl. 5 (2011), 189–206.

K. Yano: On the torse-forming directions in Riemannian spaces. Proc. Imp. Acad. Tokyo 20 (1944), 340–345.




DOI: https://doi.org/10.22190/FUMI240402028D

Refbacks

  • There are currently no refbacks.




© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)