참고문헌
-
A. M. Blaga,
$\eta$ -Ricci solitons on Lorentzian para-Sasakian manifolds, Filomat, 30(2)(2016), 489-496. https://doi.org/10.2298/FIL1602489B -
A. M. Blaga,
$\eta$ -Ricci solitons on para-Kenmotsu manifolds, Balkan J. Geom. Appl., 20(2015), 1-13. -
A. M. Blaga, S. Y. Perktas, B. L. Acet and F. E. Erdogan,
$\eta$ -Ricci solitons in ($\varepsilon$ )-almost para contact metric manifolds, Glas. Mat. Ser. III, 53(2018), 205--220. https://doi.org/10.3336/gm.53.1.14 -
C. S. Bagewadi and G. Ingalahalli, Ricci Solitons in Lorentzian
${\alpha}$ -Sasakian Manifolds, Acta Math. Acad. Paedagog. Nyhzi.(N.S.), 28(1)(2012), 59-68. - E. Bartolotti, Sulla geometria della variata a connection affine. Ann. di Mat., 4(8)(1930), 53-101. https://doi.org/10.1007/BF02428566
- A. Bejancu and K. L. Duggal, Real hypersurfaces of indefinite Kaehler manifolds, Internet. J. Math. Math. Sci., 16(1993), 545-556. https://doi.org/10.1155/S0161171293000675
- D. E. Blair, Contact manifolds in Riemannian geometry, Lecture note in Mathematics 509, Springer-Verlag, Berlin-New York, 1976.
-
S. M. Bhati, On weakly Ricci
$\phi$ -symmetric${\delta}$ -Lorentzian trans Sasakian manifolds, Bull. Math. Anal. Appl., 5 (1)(2013), 36-43. - J. T. Cho and M. Kimura, Ricci solitons and Real hypersurfaces in a complex space form, Tohoku math.J., 61(2009), 205-212. https://doi.org/10.2748/tmj/1245849443
- O. Chodosh, F. T. H. Fong, Rotational symmetry of conical Kahler-Ricci solitons, Math. Ann., 364(2016), 777-792. https://doi.org/10.1007/s00208-015-1240-x
-
U. C. De and A. Sarkar, On (
$\varepsilon$ )-Kenmotsu manifolds, Hadronic J., 32(2)(2009), 231-242. - U. C. De and A. Sarkar, On three-dimensional Trans-Sasakian Manifolds, Extracta Math., 23(2008), 265-277.
- A. Friedmann and J. Schouten, Uber die Geometric der halbsymmetrischen, Ubertra-gung, Math. Z., 21(1924), 211-223. https://doi.org/10.1007/BF01187468
- A. Gray and L. M. Harvella, The sixteen classes of almost Hermitian manifolds and their linear invariants, Ann. Mat. Pura Appl., 123(4)(1980), 35-58. https://doi.org/10.1007/BF01796539
- H. Gill and K. K. Dube, Generalized CR-Submanifolds of a trans Lorentzian para Sasakian manifold, Proc. Nat. Acad. Sci. India Sec. A Phys. Sci., 76(2006), 119-124.
- H. A. Hayden, Sub-spaces of a space with torsion, Proc. London Math. Soc., 34(1932), 27-50. https://doi.org/10.1112/plms/s2-34.1.27
- I. E. Hirica and L. Nicolescu, Conformal connections on Lyra manifolds, Balkan J. Geom. Appl., 13(2008), 43-49.
- I. E. Hirica and L. Nicolescu, On Weyl structures, Rend. Circ. Mat. Palermo (2), 53(2004), 390-400. https://doi.org/10.1007/BF02875731
- R. S. Hamilton, The Ricci flow on surfaces, Mathematics and general relativity (Santa Cruz. CA, 1986), 237-262, Contemp. Math. 71, Amer. Math. Soc., Providence, RI, 1988.
- T. Ikawa and M. Erdogan, Sasakian manifolds with Lorentzian metric, Kyungpook Math. J., 35(1996), 517-526.
- J. B. Jun, U. C. De and G. Pathak, On Kenmotsu manifolds, J. Korean Math. Soc., 42(3)(2005), 435-445. https://doi.org/10.4134/JKMS.2005.42.3.435
- H. Levy, Symmetric tensors of the second order whose covariant derivatives vanish, Ann. Math., 27(2)(1925), 91-98. https://doi.org/10.2307/1967964
- J. C. Marrero, The local structure of Trans-Sasakian manifolds, Ann. Mat. Pura Appl., 162(1992), 77-86. https://doi.org/10.1007/BF01760000
- K. Matsumoto, On Lorentzian paracontact manifolds, Bull. Yamagata Univ. Natur. Sci., 12(1989), 151-156.
- H. G. Nagaraja and C.R. Premalatha, Ricci solitons in Kenmotsu manifolds, J. Math. Anal., 3 (2)(2012), 18-24.
- J. A. Oubina, New classes of almost contact metric structures, Publ. Math. Debrecen, 32(1985), 187-193.
- G. Pathak and U. C. De, On a semi-symmetric metric connection in a Kenmotsu manifold, Bull. Calcutta Math. Soc., 94(4)(2002), 319-324.
- S. S. Pujar and V. J. Khairnar, On Lorentzian trans-Sasakian manifold-I, Int. J. of Ultra Sciences of Physical Sciences, 23(1)(2011), 53-66.
- S. S. Pujar, On Lorentzian Sasakian manifolds, Antactica J. Math., 8(2012), 30-38.
-
R. Sharma, Certain results on K-contact and (
${\kappa},\,{\mu}$ )-contact manifolds, J. Geom., 89(1-2)(2008), 138-147. https://doi.org/10.1007/s00022-008-2004-5 - A. Sharfuddin and S. I. Hussain, Semi-symmetric metric connections in almost contact manifolds, Tensor (N.S.), 30(1976), 133-139.
-
S. S. Shukla and D. D. Singh, On (
$\varepsilon$ )-trans-Sasakian manifolds, Int. J. Math. Anal., 4(49-52)(2010), 2401-2414. -
M. D. Siddiqi, A. Haseeb and M. Ahmad, On generalized Ricci-recurrent (
$\varepsilon,\;{\delta}$ )-trans-Sasakian manifolds, Palest. J. Math., 4(1)(2015), 156-163. - M. M. Tripathi, On a semi-symmetric metric connection in a Kenmotsu manifold, J. Pure Math., 16(1999), 67-71.
- M. M. Tripathi, E. Kilic, S. Y. Perktas and S. Keles, Indefnite almost para-contact metric manifolds, Int. J. Math. Math. Sci., (2010), Art. ID 846195, 19 pp. https://doi.org/10.1155/IJMMS.2005.19
- T. Takahashi, Sasakian manifold with Pseudo-Riemannian metric, Tohoku Math. J., 21(1969), 271-290. https://doi.org/10.2748/tmj/1178242996
- S. Tanno, The automorphism groups of almost contact Riemannian manifolds, Tohoku Math. J., 21(1969), 21-38. https://doi.org/10.2748/tmj/1178243031
-
K. Venu and H.G. Nagaraja,
$\eta$ -Ricci solitons in trans-Sasakian manifolds, Commun. Fac. sci. Univ. Ank. Ser. A1 Math. Stat., 66(2)(2017), 218-224. -
X. Xufeng and C. Xiaoli, Two theorems on
$\varepsilon$ -Sasakian manifolds, Internat. J. Math. Math. Sci., 21(1998), 249-254. https://doi.org/10.1155/S0161171298000350 -
A. F. Yaliniz, A. Yildiz and M. Turan, On three-dimensional Lorentzian
${\beta}$ -Kenmotsu manifolds, Kuwait J. Sci. Engrg., 36(2009), 51-62. -
A. Yildiz, M. Turan, M. and C. Murathan, A class of Lorentzian
${\alpha}$ -Sasakian manifolds, Kyungpook Math. J., 49(2009), 789-799. https://doi.org/10.5666/KMJ.2009.49.4.789 - K. Yano, On semi-symmetric metric connections, Rev. Roumaine Math. Pures Appl., 15(1970), 1579-1586.
- K. Yano and M. Kon, Structures on Manifolds, Series in Pure Mathematics 3, World Scientific Publishing, Singapore, 1984.