EXISTENCE OF N(k)-QUASI EINSTEIN MANIFOLDS
Abstract
The aim of the present paper is to study the properties of pseudo Ricci symmetric
quasi Einstein and N(k)-quasi Einstein manifolds. We construct some examples of
N(k)-quasi Einstein manifolds which support the existence of such manifolds.
Keywords
Keywords
Full Text:
PDFReferences
K. Yano: Concircular geometry I. concircular transformations. Proc. Imp. Acad. Tokyo 16 (1940), 195-200.
K. Yano and S. Bochner: Curvature and betti numbers. Annals of Mathematics studies 32 (Princeton University Press), 1953.
K. Yano and M. Kon: Structures on manifolds. Series in Pure Mathematics, World Scientific Publishing Co., Singapore, 1984.
M. C. Chaki and R. K. Maithy: On quasi Einstein manifolds. Publ. Math. Debrecen 57, no. 3-4 (2000), 297-306.
D. E. Blair: Riemannian geometry of contact and symplectic manifolds. Progress in Mathematics 203, Birkhauser Boston , Inc., Boston, MA, 2002.
M. Okumura: Some remarks on space with a certain contact structure. Tohoku Math. J. 14 (1962), 135-145.
S. Tanno: Ricci curvatures of contact Riemannian manifolds. Tohoku Math. J. 40 (1988), 441-417.
U. C. De and G. C. Ghosh: On quasi Einstein manifolds II. Bull. Calcutta Math. Soc. 96, 2 (2004), 135-138.
M. M. Tripathi and J. S. Kim: On N(k)−quasi Einstein manifolds. Commun. Korean Math. Soc. 22, no. 3 (2007), 411-417.
Ozgür Cihan and M. M. Tripathi: On the concircular curvature tensor of an N(k)−quasi Einstein manifolds. Math. Pann. 18, 1 (2007), 95-100.
Ozgür Cihan and Sibel Sular: On N(k)−quasi Einstein manifolds satisfying certain conditions. Balkan J. Jeom. Appl. 13, 2 (2008), 74-79.
Ozgür Cihan: N(k)−quasi Einstein manifolds satisfying certain conditions. Chao, Solitons Fractals 38, 5 (2008), 1373-1377.
R. N. Singh, M. K. Pandey and D. Gautam: On N(k)−quasi Einstein manifolds. Novi Sad J. Math. 40, 2 (2010), 23-28.
A. De, U. C. De and A. K. Gazi: On a class of N(k)−quasi Einstein manifolds. Commun. Korean Math. Soc. 26, 4 (2011), 623-634.
A. Yildiz, U. C. De and A. Centinkaya: N(k)−quasi Ein-
stein manifolds satisfying certain curvature conditions. (2011) [http :
//www.emis.de/journals/BMMSS/pdf/acceptedpapers/2011−10−043 R 1.pdf].
A. Taleshian and A. A. Hosseinzadeh: Investigation of some conditions on N(k)−quasi Einstein manifolds. Bull. Malays. Math. Sci. Soc. 34 3 (2011), 455-
A. Taleshian and A. A. Hosseinzadeh: On W 2 curvature tensor N(k)−quasi Einstein manifolds. J. Math. Comp. Sci. 1 (2010), 28-32.
U. C. De and G. C. Ghosh: On quasi Einstein and special quasi Einstein manifolds. In: Proc. of the Int. conf. of Mathematics and its applications, Kuwait
University, April 5-7, 2004, 178-191.
R. Deszcz, M. Hotlos and Z. Senturk: On curvature properties of quasi-Einstein hypersurfaces in semi-Euclidean spaces. Soochow J. Math. 27 (2001),
-389.
C. A. Mantica and Y. J. Suh: Conformally symmetric manifolds and quasi conformally recurrent Riemannian manifolds. Balkan Journal of Geometry and
its Applications 16 (2011), 66-77.
L. Tamassy and T. Q. Binh: On weak symmetries of Einstein and Sasakian manifolds. Tensor N. S. 53 (1993), 140-148.
Y. Yang and S. Xu: Some conditions of N(k)−quasi Einstein manifolds. Int. J. Dig. Cont. Tech. Appl. 6, 8 (2012), 144-150.
A. A. Hosseinzadeh and A. Taleshian: On conformal and quasi conformal curvature tensors of an N(k)−quasi Einstein manifolds. Commun. Korean Math. Soc. 27, 2 (2012), 317-326.
M. K. Dwivedi: A study of W 2 curvature tensor of a N(k)−quasi Einstein manifold. 5-IJSET 1 (2010), 1-3.
P. Debnath and A. Konar: On quasi Einstein manifold and quasi Einstein spacetime. Differential Geometry-Dynamical Systems 12 (2010), 73-82.
M. C. Chaki: On generalized quasi Einstein manifolds. Publ. Math. Debrecen 58 (2001), 683-691.
U. C. De and G. C. Ghosh: On quasi Einstein manifolds. Period. Math. Hungar. 48 (2004), 223-231.
S. Guha: On quasi Einstein and generalized quasi Einstein manifolds. Facta Univ. Ser. Mech. Automat. Control Robot 3 14 (2003), 821-842.
M. C. Chaki: On pseudo Ricci symmetric manifolds. Bulg. J. Phisics 15 (1988), 526-531.
R. N. Sen and M. C. Chaki: On curvature restriction of a certain kind of conformally flat Riemannian spaces of class one. Proc. Nat. Inst. Sci. India Part
A 33 (1967), 100-102.
Sinem Güler and Sezgin Altay Demirba˘ g: On Ricci symmetric generalized quasi-Einstein space times. Miskolc Mathematical Notes 16 (2015), 853-868.
A. A. Shaikh, Dae Won Yoon and S. K. Hui: On quasi-Einstein space times. Tsukuba J. Math. 33 (2009), 305-326.
A. A. Shaikh, Young Ho Kim and S. K. Hui: On Lorentzian quasi-Einstein manifolds. J. Korean Math. Soc. 48 (2011), 669-689.
G. P. Pokhariyal and R. S. Mishra: Curvature tensor and their relativistic significance II. Yokohama Mathematical Journal, 19 (1971), 97-103.
R. H. Ojha: M−projectively flat Sasakian manifolds. Indian J. Pure Appl. Math. 17 4 (1986), 481-484.
R. H. Ojha: A note on the M−projective curvature tensor. Indian J. Pure Appl. Math. 8 12 (1975), 1531-1534.
S. K. Chaubey and R. H. Ojha: On the m−projective curvature tensor of a Kenmotsu manifold. Differential Geometry - Dynamical Systems 12 2010, 52-60.
S. K. Chaubey: Some properties of LP−Sasakian manifolds equipped with m−projective curvature tensor. Bulletin of Math. Analysis and Applications 3 (4)
(2011), 50-58.
S. K. Chaubey: On weakly m−projective symmetric manifolds. Novi Sad J. Math. 42 (2012), 67-79.
S. K. Chaubey, S. Prakash and R. Nivas: Some properties of m−projective curvature tensor in Kenmotsu manifolds. Bulletin of Math. Analysis and Appli-
cations 4 (3) (2012), 48-56.
P. Alegre, David E. Blair and A. Carriazo: Generalized Sasakian Space forms. Israel J. of Math. 141 (2004), 157-183.
DOI: https://doi.org/10.22190/FUMI1703369C
Refbacks
ISSN 0352-9665 (Print)