Open Access
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A Non-Flat Riemannian Manifold Admitting Certain Vectors Fields
*Santu DeyCorresponding authorsantujumath6@gmail.comDepartment of MathematicsJadavpur UniversityKolkata, West Bengal, 700032, IndiaView full profile → , Buddhadev Palpal.buddha@gmail.comDepartment of MathematicsInstitute of ScienceBanaras Hindu University, Varanasi, Uttar Pradesh, 221005, IndiaView full profile → , Arindam Bhattacharyyabhattachar1968@yahoo.co.inDepartment of MathematicsJadavpur UniversityKolkata, West Bengal, 700032, IndiaView full profile →
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- Received:
- 25 Oct 2017
- Accepted:
- 12 Nov 2018
- Published Online:
- 18 Nov 2019
- Article type:
- Article
- Language:
- EN
- Article no.:
- 1726037X.2019.1668148
- Pages:
- 221–237
Abstract
It is well-known that Einstein manifolds play an important role in geometry as well as in general relativity. Einstein manifolds form a natural subclass of the class of quasi-Einstein manifolds. The object of the present paper is to study some geometric properties of mixed-generalized quasi-Einstein Manifolds (MG(QE)undefined) which admitting certain vector fields. We show the existence of MG(QE)undefined, by constructing several non-trivial examples. Finally we study warped product on MG(QE)undefined and show that M = I×M∗ (dimI = 1 and dimM∗ = n − 1) is a MG(QE)undefined if M∗ is a generalized quasi-Einstein Manifold (G(QE)undefined).
Keywords
Subject Classifications
53C2553C15
References
- A.Bhattacharyya, T.De, . Diff. Geom.-Dyn. Syst . 2007 ; 9 : 40 - 46 .
- R. L.Bishop and B.ONeill, , Trans. Amer. Math. Soc ., 145 ( 1969 ), 1 - 49 . doi: 10.1090/S0002-9947-1969-0251664-4
- M. C.Chaki and R. K.Maity, , Publ. Math. Debrecen 57 ( 2000 ), 297 - 306 .
- U. C.De and G. C.Ghosh, , Kyungpook Math. J . 44 ( 2004 ), 607 - 615 .
- U. C.De, N.Guha and D.Kamilya, , Tensor(N.S .), 56 ( 1995 ), 312 - 317 .
- S.Dey and A.Bhattacharyya, Conformal mappings of mixed generalized quasi-Einstein man- ifolds admitting special vector fields , Extracta Math . 32 ( 2 ) ( 2017 ), 255 - 273 .
- A.Gray, , Geom. Dedicate 7 ( 1998 ), 259 - 280 .
- S.Güler and A.Demirbǎg, , Filomat 29 : 3 ( 2015 ), 443 - 456 . doi: 10.2298/FIL1503443G
- G. I.Kručkovič, , Dokl. Akad. Nauk SSSR 115 ( 1957 ), 862 - 865 (in Russian) .
- E. M.Patterson, , Journal London Math. Soc ., 27 ( 1952 ), 287 - 295 . doi: 10.1112/jlms/s1-27.3.287
- J. A.Schouten, Ricci-Calculus , Springer , Berlin, 1954 .
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