SOME RESULTS ON YAMABE SOLITONS ON NEARLY HYPERBOLIC SASAKIAN MANIFOLDS

Sunil Kumar Yadav, Mohd. Danish Siddiqi, D. L. Suthar

DOI Number
https://doi.org/10.22190/FUMI210128014Y
First page
201
Last page
221

Abstract


We classify almost Yamabe on nearly hyperbolic Sasakian manifolds whose potential vector field is torse-forming admitting semi-symmetric metric connection and quarter symmetric non-metric connection. Certain results of such solitons on CR-submanifolds of nearly hyperbolic Sasakian manifolds with respect to such connection are obtained. Finally, a non-trivial example is given to validate some of our results.


Keywords

Sasakian manifolds, CR-sub-manifolds, Yamabe solitons.

Full Text:

PDF

References


M. Ahmad, M. D. Siddiqi, and S. Rizvi: CR-sub-manifolds of a nearly hyperbolic Sasakian manifold admitting semi-symmetric semi-metric connection. International J. Math. Sci. and Engg. Appls. 6 (2012), 145-155.

E. Barbosa and E. Ribeiro: On conformal solution of the Yamabe flow. Arch. Math. 101 (2013), 79-89.

A. Bejancu: CR-sub-manifolds of a Ka¨hler manifold I, Proc. Amer. Math. Soc. 69 (1978), 135-142.

A. Bejancu: Geometry of CR-sub-manifolds. D. Reidel Publ. Co., 1986.

A. Bejancu and N. Papaghuic: CR-sub-manifolds of Kenmotsu manifold. Rend. Mat. 7 (1984), 607-622.

L. Bhatt and K. K. Dube: CR-sub-manifolds of trans-hyperbolic Sasakian manifold. Acta Ciencia Indica 31 (2003), 91-96.

D. E. Blair: Contact manifolds in Riemannian geometry. Lecture Notes in Mathematics, Vol. 509, Springer-Verlag, Berlin, 1976.

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

B. Y. Chen and S. Deshmukh: Yamabe and quasi-Yamabe solitons on Euclidean sub-manifolds. Mediterr. J. Math. 15 (2018), 1-9.

L. S. K. Das and M. Ahmad: CR-sub-manifolds of a Lorentzian para-Sasakian manifold endowed with a semi-symmetric non-metric connection. Algebras Group Geometry 31 (2014), 313-326.

P. Daskalopoulos and N. Sesum: The classification of locally conformally flat Yamabe solitons. Adv. Math. 240 (2013), 346-369.

S. Deshmukh and B.Y. Chen: A note on Yamabe solitons. Balkan J. Geom. and Appl. 23 (2018), 37-43.

S. Golab: On semi-symmetric and quarter symmetric linear connections. Tensor, N.S., Japan, (1975), 249-254.

R. S. Hamilton: The Ricci flow on surfaces, in: Mathematics and General Relativity. in: Contemp. Math., 71, (1986), 237-262.

C. J. Hsu: On CR-sub-manifolds of Sasakian manifolds I, Math. Research Center Reports, Symposium Summer, (1983), 117-140.

S. Y. Hsu: A note on compact gradient Yamabe solitons. J. Math. Anal. Appl. 388 (2012), 725-726.

M. Kobayashi: CR-sub-manifolds of a Sasakian manifold. Tensor (N.S.), Japan, (1981), 297-307.

M. D. Siddiqi, M. Ahmed and J. P. Ojha: CR-sub-manifolds of nearly-trans hyperbolic sasakian manifolds admitting semi symmetric-non-metric connection. African J. Diaspora bf 17(10) (2014), 93-105.

M. D. Upadhyay and K. K. Dubey: Almost contact hyperbolic (f, ξ, η, g)-structure. Acta. Math. Acad. Scient. Hung. Tomus, 28 (1976), 1-4.

K. Yano: On semi-symmetric metric connection. Rev. Roum. Math. Pureset Appl. 15 (1970), 1579-1586.

K. Yano: On torse-forming direction in a Riemannian space. Proc. Imp. Acad. Tokyo 20 (1944), 340-345.

K. Yano and B. Y. Chen: On concurrent vector fields of immersed manifolds. Kodai Math. Sem. Rep. bf 23 (1971), 343-350.

K. Yano and M. Kom: Contact CR-sub-manifolds. Kodai Math. J. (1982), 238-252.




DOI: https://doi.org/10.22190/FUMI210128014Y

Refbacks

  • There are currently no refbacks.




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