참고문헌
-
S. R. Ashoka, C. S. Bagewadi, and G. Ingalahalli, Certain results on Ricci solitons in
$\alpha$ -Sasakian manifolds, Hindawi Publ. Corporation, Geometry 2013 (2013), Article ID 573925, 4 pages. -
S. R. Ashoka, C. S. Bagewadi, and G. Ingalahalli, A geometry on Ricci solitons in
$(LCS)_n$ -manifolds, Differ. Geom. Dyn. Syst. 16 (2014), 50-62. - M. Atceken, On geometry of submanifolds of (LCS)n-manifolds, Int. J. Math. Math. Sci. 2012 (2012), Art. ID 304647, 11 pp.
- M. Atceken and S. K. Hui, Slant and pseudo-slant submanifolds of LCS-manifolds, Czechoslovak Math. J. 63 (2013), no. 1, 177-190. https://doi.org/10.1007/s10587-013-0012-6
- C. S. Bagewadi and G. Ingalahalli, Ricci solitons in Lorentzian-Sasakian manifolds, Acta Math. Acad. Paedagog. Nyhazi. 28 (2012), no. 1, 59-68.
- C. L. Bejan and M. Crasmareanu, Ricci solitons in manifolds with quasi constant curvature, Publ. Math. Debrecen 78 (2011), no. 1, 235-243. https://doi.org/10.5486/PMD.2011.4797
- M. C. Chaki, On pseudo Ricci symmetric manifolds, Bulgar. J. Phys. 15 (1988), 526-531.
- B. Y. Chen and S. Deshmukh, Geometry of compact shrinking Ricci solitons, Balkan J. Geom. Appl. 19 (2014), no. 1, 13-21.
-
S. K. Hui, On
$\phi$ -pseudo symmetries of$(LCS)_n$ -manifolds, Kyungpook Math. J. 53 (2013), no. 2, 285-294. https://doi.org/10.5666/KMJ.2013.53.2.285 -
S. K. Hui and M. Atceken, Contact warped product semi-slant submanifolds of
$(LCS)_n$ -manifolds, Acta Univ. Sapientiae Math. 3 (2011), no. 2, 212-224. -
G. Ingalahalli and C. S. Bagewadi, Ricci solitons in
$\alpha$ -Sasakian manifolds, ISRN Ge-ometry 2012 (2012), Article ID 421384, 13 pages. - H. Levy, Symmetric tensors of the second order whose covariant derivatives vanish, Ann. of Math. 27 (1925), no. 2, 91-98. https://doi.org/10.2307/1967964
- K. Matsumoto, On Lorentzian almost paracontact manifolds, Bull. Yamagata Univ. Nat. Sci. 12 (1989), 151-156.
- I. Mihai and R. Rosca, On Lorentzian para-Sasakian manifolds, Classical Anal., 155-169, World Sci. Publ., Singapore, 1992.
- H. G. Nagaraja and C. R. Premlatta, Ricci solitons in Kenmotsu manifolds, J. Math. Anal. 3 (2012), no. 2, 18-24.
-
D. Narain and S. Yadav, On weak concircular symmetries of
$(LCS)_{2n+1}$ -manifolds, Global J. Sci. Frontier Research 12 (2012), 85-94. - B. O'Neill, Semi Riemannian Geometry with Applications to Relativity, Academic Press, New York, 1983.
-
D. G. Prakasha, On Ricci
$\eta$ -recurrent$(LCS)_n$ -manifolds, Acta Univ. Apulensis Math. Inform. 24 (2010), 109-118. - A. A. Shaikh, On Lorentzian almost paracontact manifolds with a structure of the concircular type, Kyungpook Math. J. 43 (2003), no. 2, 305-314.
-
A. A. Shaikh, Some results on
$(LCS)_n$ -manifolds, J. Korean Math. Soc. 46 (2009), no. 3, 449-461. https://doi.org/10.4134/JKMS.2009.46.3.449 -
A. A. Shaikh and H. Ahmad, Some transformations on
$(LCS)_n$ -manifolds, Tsukuba J. Math. 38 (2014), no. 1, 1-24. https://doi.org/10.21099/tkbjm/1407938669 - A. A. Shaikh and K. K. Baishya, On concircular structure spacetimes, J. Math. Stat. 1 (2005), no. 2, 129-132. https://doi.org/10.3844/jmssp.2005.129.132
- A. A. Shaikh and K. K. Baishya, On concircular structure spacetimes II, Amer. J. Appl. Sci. 3 (2006), no. 4, 1790-1794. https://doi.org/10.3844/ajassp.2006.1790.1794
-
A. A. Shaikh, T. Basu, and S. Eyasmin, On locally
$\phi$ -symmetric$(LCS)_n$ -manifolds, Int. J. Pure Appl. Math. 41 (2007), no. 8, 1161-1170. -
A. A. Shaikh, T. Basu, and S. Eyasmin, On the existence of
$\phi$ -recurrent$(LCS)_n$ -manifolds, Extracta Math. 23 (2008), no. 1, 71-83. -
A. A. Shaikh and T. Q. Binh, On weakly symmetric
$(LCS)_n$ -manifolds, J. Adv. Math. Stud. 2 (2009), no. 2, 103-118. -
A. A. Shaikh and S. K. Hui, On generalized
$\phi$ -recurrent$(LCS)_n$ -manifolds, AIP Conf. Proc. 1309 (2010), 419-429. - R. Sharma, Second order parallel tensor in real and complex space forms, Internat. J. Math. Math. Sci. 12 (1989), no. 4, 787-790. https://doi.org/10.1155/S0161171289000967
- R. Sharma, Second order parallel tensor on contact manifolds, Algebras Groups Geom. 7 (1990), no. 2, 145-152.
-
R. Sharma, Certain results on k-contact and (k,
$\mu$ )-contact manifolds, J. Geom. 89 (2008), no. 1-2, 138-147. https://doi.org/10.1007/s00022-008-2004-5 -
T. Takahashi, Sasakian
$\phi$ -symmetric spaces, Tohoku Math. J. 29 (1977), no. 1, 91-113. https://doi.org/10.2748/tmj/1178240699 - M. M. Tripathi, Ricci solitons in contact metric manifolds, arxiv:0801.4221[Math.DG] (2008).
- K. Yano, Concircular geometry I. Concircular transformations, Proc. Imp. Acad. Tokyo 16 (1940), 195-200. https://doi.org/10.3792/pia/1195579139