TARU PUBLICATIONS
Journal of Dynamical Systems and Geometric Theories cover

Journal of Dynamical Systems and Geometric Theories

(Since 2002)
Open Access ·Peer-reviewed·ISSN (Online): 2169-0057·ISSN (Print): 1726-037X
Powered by:Powered by

The Journal of Dynamical Systems and Geometric Theories (JDSGT) is a world leading journal publishing high quality, rigorously peer-reviewed original research on dynamical systems and geometry, including the interactions between these two subjects and interdisciplinary research with other branches of knowledge since 2003. Topics published by the Journal include but are not limited to: Random dynamical systems Geometry and physics Dynamical systems with hyperbolic behaviour Real and complex geometry Ergodic theory Distance geometry Topological dynamics Global differential geometry Infinite-dimensional Hamiltonian systems Symplectic geometry, contact geometry The journal considers original research articles, survey articles, and book reviews for publication. Responses to articles and correspondence will also be considered at the Chief Editor’s discretion.

Issues up to 2022 co-published with and available at:Taylor & Francis
info@tarupublications.com
Taru Online First Current IssueBrowse all Issues
Journal of Dynamical Systems and Geometric Theories
Open Access Article

A Non-Flat Riemannian Manifold Admitting Certain Vectors Fields

* , ,

* Corresponding author · click or hover a name for details

pp. 221–237Vol. 17Issue 2July 2019DOI: 10.1080/1726037X.2019.1668148XML
Received:
25 Oct 2017
Accepted:
12 Nov 2018
Published Online:
03 Jul 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

Mixed-generalized quasi-Einstein manifoldsCodazzi type of Ricci tensorcyclic parallel Ricci tensorKilling vector fieldconcurrent vector fieldre- current vector fieldwarped product manifold

Subject Classifications

53C2553C15

References

A.Bhattacharyya, T.De, On mixed generalized quasi-Einstein manifolds. Diff. Geom.-Dyn. Syst . 2007 ; 9 : 40 - 46 . R. L.Bishop and B.ONeill, Manifolds of negative curvature, Trans. Amer. Math. Soc ., 145 ( 1969 ), 1 - 49 . doi: 10.1090/S0002-9947-1969-0251664-4 M. C.Chaki and R. K.Maity, On quasi-Einstein manifolds, Publ. Math. Debrecen 57 ( 2000 ), 297 - 306 . U. C.De and G. C.Ghosh, On generalized quasi-Einstein manifolds, Kyungpook Math. J . 44 ( 2004 ), 607 - 615 . U. C.De, N.Guha and D.Kamilya, On generalized Ricci-recurrent manifolds, 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, Einstein-like manifolds which are not Einstein, Geom. Dedicate 7 ( 1998 ), 259 - 280 . S.Güler and A.Demirbǎg, On some classes of generalized quasi-Einstein manifolds, Filomat 29 : 3 ( 2015 ), 443 - 456 . doi: 10.2298/FIL1503443G G. I.Kručkovič, On semi-reducible Riemannian spaces, Dokl. Akad. Nauk SSSR 115 ( 1957 ), 862 - 865 (in Russian) . E. M.Patterson, Some theorems on Ricci-recurrent spaces, Journal London Math. Soc ., 27 ( 1952 ), 287 - 295 . doi: 10.1112/jlms/s1-27.3.287 J. A.Schouten, Ricci-Calculus , Springer , Berlin, 1954 .
Views: 8Downloads: 5Citations: 0