참고문헌
- A. Bejancu and K. L. Duggal, Real hypersurfaces of indefinite Kaehler manifolds, Int. J. Math. Math. Sci., 16 (1993), 545-556. https://doi.org/10.1155/S0161171293000675
-
A. Haseeb, Some results on projective curvature tensor in an
${\epsilon}$ -Kenmotsu manifold, Palestine J. Math., 6(Special Issue: II) (2017), 196-203. -
A. Haseeb, A. Prakash and M. D. Siddiqi, On a quarter-symmetric metric connec- tion in an
${\epsilon}$ -Lorentzian para-Sasakian manifold, Acta Math. Univ. Comenianae, 86(1) (2017), 143-152. -
A. Haseeb, M. A. Khan. and M. D. Siddiqi, Some more results on an
${\epsilon}$ -Kenmotsu manifold with a semi-symmetric metric connection, Acta Math. Univ. Comenianae, 85(1) (2016), 9-20. -
A. Singh and S. Kishor, Some types of
${\eta}$ -Ricci solitons on Lorentzian para-Sasakian manifolds, Facta Universitatis (NIS), 33(2) (2018), 217-230. -
A. M. Blaga,
${\eta}$ -Ricci solitons on Lorentzian para-Sasakian manifolds, Filomat, 30(2) (2016), 489-496. https://doi.org/10.2298/FIL1602489B - B. O'Neill, Semi-Riemannian geometry with applications to relativity, Academic Press, New York-London, 1983.
-
D. G. Prakasha and B. S. Hadimani,
${\eta}$ -Ricci solitons on para-Sasakian manifolds, J. Geom., 108 (2017), 383-392. https://doi.org/10.1007/s00022-016-0345-z - G. Perelman, The entropy formula for the Ricci flow and its geometric applications, http://arXiv.org/abs/math/0211159, 2002, 1-39.
- G. Perelman, Ricci flow with surgery on three manifolds, http://arXiv.org/abs/math/0303109, 2003, 1-22.
- J. T. Cho and M. Kimura, Ricci solitons and real hypersurfaces in a complex space form, Tohoku Math. J., 61(2) (2009), 205-212. https://doi.org/10.2748/tmj/1245849443
- K. Mandal and U. C. De, Quarter-symmetric metric connection in a P-Sasakian manifold, Analele Univ. de Vest, Timisoara Seria Matematica-Informatica, LIII(1) (2015), 137-150.
- K. Yano and M. Kon, Structures on Manifolds, Series in Pure Math., Vol. 3, World Sci., 1984.
- M. Ahmad, J. B. Jun, and A. Haseeb, Hypersurfaces of almost r-paracontact Riemannian manifold with a quarter symmetric metric connection, Bull. Korean Math. Soc., 46(3) (2009), 477-487. https://doi.org/10.4134/BKMS.2009.46.3.477
- M. Ali and Z. Ahsan, Gravitational field of Schwarzschild soliton, Arab J. Math. Sci., 21 (2015), 15-21. https://doi.org/10.1016/j.ajmsc.2013.10.003
- M. M. Tripathi, E. Kilic, S. Y. Perktas and S. Keles, Indefinite almost para-contact metric manifolds, Int. J. Math. and Math. Sci., (2010), Article ID: 846195, 19 pages.
- R. Prasad and A. Haseeb, Conformal curvature tensor on K-contact manifolds with respect to the quarter symmetric metric connection, Facta Universitatis (NIS), Ser. Math. Inform., 32 (2017), 503-514.
-
R. Prasad and V. Srivastava, On
${\epsilon}$ -Lorentzian para-Sasakian manifolds, Commun. Korean Math. Soc., 27 (2012), 297-306. https://doi.org/10.4134/CKMS.2012.27.2.297 -
R. Sharma, Certain results on K-contact and (K,
${\mu}$ )-contact manifolds, J. Geom., 89 (2008), 138-147. https://doi.org/10.1007/s00022-008-2004-5 - R. N. Singh and S. K. Pandey, On quarter-symmetric metric connection in an LP-Sasakian manifold, Thai J. Math., 12 (2014), 357-371.
-
R. N. Singh, S. K. Pandey, G. Pandey and K. Tiwari, On a semi-symmetric metric connection in an
${\epsilon}$ -Kenmotsu manifold, Commun. Korean Math. Soc., 29 (2014), 331-343. https://doi.org/10.4134/CKMS.2014.29.2.331 - R. S. Hamilton, The Ricci flow on surfaces, Mathematics and general relativity, Contemp. Math., 71, American Math. Soc., (1988), 237-262.
- R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Diff. Geom., 17 (1982), 255-306. https://doi.org/10.4310/jdg/1214436922
- S. Deshmukh, H. Alodan and H. Al-Sodais, A note on Ricci solitons, Balkan J. Geom. Appl., 16 (2011), 48-55.
- S. Golab, On semi-symmetric and quarter-symmetric linear connections, Tensor (N.S.), 29(1975), 249-254.
- U. C. De, Ricci soliton and gradient Ricci soliton on P-Sasakian manifolds, The Aligarh Bull. of Maths., 29 (2010), 29-34.
-
U. C. De and A. Sarkar, On
${\epsilon}$ -Kenmotsu manifold, Hardonic J., 32 (2009), 231-242. - U. C. De and A. K. Mondal, Quarter-symmetric metric connection on 3-dimensional quasi-Sasakian manifolds, SUT J. Math., 46 (2010), 35-52.
-
X. Xufeng and C. Xiaoli, Two theorems on
${\epsilon}$ -Sasakian manifolds, Int. J. Math. Math. Sci., 21 (1998), 249-54. https://doi.org/10.1155/S0161171298000350