| Title:
|
On the existence of generalized quasi-Einstein manifolds (English) |
| Author:
|
De, Uday Chand |
| Author:
|
Mallick, Sahanous |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
47 |
| Issue:
|
4 |
| Year:
|
2011 |
| Pages:
|
279-291 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The object of the present paper is to study a type of Riemannian manifold called generalized quasi-Einstein manifold. The existence of a generalized quasi-Einstein manifold have been proved by non-trivial examples. (English) |
| Keyword:
|
quasi-Einstein manifolds |
| Keyword:
|
generalized quasi-Einstein manifold |
| Keyword:
|
manifold of generalized quasi-constant curvature |
| Keyword:
|
manifold of quasi-constant curvature |
| MSC:
|
53C25 |
| idZBL:
|
Zbl 1249.53063 |
| idMR:
|
MR2876950 |
| . |
| Date available:
|
2011-12-16T15:16:32Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141776 |
| . |
| Reference:
|
[1] Bejan, C., Binh, T. Q.: Generalized Einstein manifolds.WSPC–Proceeding Trim Size, dga 2007, 2007, pp. 47–54. |
| Reference:
|
[2] Besse, A. L.: Einstein manifolds.Ergeb. Math. Grenzgeb., 3. Folge, Bd. 10, Springer–Verlag, Berlin, Heidelberg, New York, 1987. Zbl 0613.53001, MR 0867684 |
| Reference:
|
[3] Blair, D. E.: Riemannian geometry of contact and symplectic manifolds.Birkhauser, Boston, 2002. Zbl 1011.53001, MR 1874240 |
| Reference:
|
[4] Chaki, M. C.: On generalized quasi–Einstein manifolds.Publ. Math. Debrecen 58 (2001), 683–691. Zbl 1062.53035, MR 1828719 |
| Reference:
|
[5] Chaki, M. C.: On super quasi–Einstein manifolds.Publ. Math. Debrecen 64 (2004), 481–488. Zbl 1093.53045, MR 2059079 |
| Reference:
|
[6] Chaki, M. C., Maity, R. K.: On quasi–Einstein manifolds.Publ. Math. Debrecen 57 (2000), 297–306. Zbl 0968.53030, MR 1798715 |
| Reference:
|
[7] Chen, B. Y.: Geometry of submanifolds.Marcel Dekker. Inc., New York, 1973. Zbl 0262.53036, MR 0353212 |
| Reference:
|
[8] Chen, B. Y.: Geometry of submanifolds and its applications.Science University of Tokyo, 1981. Zbl 0474.53050, MR 0627323 |
| Reference:
|
[9] Chen, B. Y., Yano, K.: Hypersurfaces of a conformally flat space.Tensor N. S. 26 (1972), 318–322. Zbl 0257.53027, MR 0331283 |
| Reference:
|
[10] Das, Lovejoy: On generalized $p$–quasi–Einstein manifolds.preprint. Zbl 1159.53325 |
| Reference:
|
[11] De, U. C., Gazi, A. K.: On nearly quasi–Einstein manifolds.Novi Sad J. Math. 38 (2) (2008), 115–121. MR 2526034 |
| Reference:
|
[12] De, U. C., Ghosh, G. C.: On generalized quasi–Einstein manifolds.Kyungpook Math. J. 44 (2004), 607–615. Zbl 1076.53509, MR 2108466 |
| Reference:
|
[13] De, U. C., Ghosh, G. C.: On quasi–Einstein and special quasi–Einstein manifolds.Proc. of the Int. Conf. of Mathematics and its Applications, Kuwait University, April 5–7, 2004, 2004, pp. 178–191. MR 2143298 |
| Reference:
|
[14] Deszcz, R., Hotlos, M., Senturk, Z.: On curvature properties of quasi–Einstein hypersurfaces in semi–Euclidean spaces.Soochow J. Math. 27 (2001), 375–389. Zbl 1008.53020, MR 1867806 |
| Reference:
|
[15] Mocanu, A. L.: Les variétés à courbure quasi-constante de type Vranceanu (French).rench), Proceedings of the National Conference on Geometry and Topology (1986), Univ. Bucureşti, Bucharest, 1988, Manifolds with quasiconstant curvature of Vranceanu type, pp. 163–168. MR 0980015 |
| Reference:
|
[16] Muelemeester, W. De, Verstraelen, L.: Codimension 2 submanifolds with 2–quasi–umbilical normal direction.J. Korean Math. Soc. 15 (1979), 101–108. |
| Reference:
|
[17] Patterson, E. M.: Some theorems on Ricci–recurrent spaces.J. London Math. Soc. 27 (1952), 2887–295. Zbl 0048.15604, MR 0048891 |
| Reference:
|
[18] Shaikh, A. A.: On pseudo quasi–Einstein manifolds.Periodica Mathematica Hungarica 59 (2) (2009), 119–146. Zbl 1224.53029, MR 2587857, 10.1007/s10998-009-0119-6 |
| Reference:
|
[19] Tamassay, L., Binh, T. Q.: On weak symmetries of Einstein and Sasakian manifolds.Tensor N. S. 53 (1993), 140–148. MR 1455411 |
| Reference:
|
[20] Vranceanu, Gh.: Lecons des Geometrie Differential.Ed. de L'Academie, vol. 4, Bucharest, 1968. |
| Reference:
|
[21] Yano, K., Sawaki, S.: Riemannian manifolds admitting a conformal transformation group.J. Differential Geom. 2 (1968), 161–184. Zbl 0167.19802, MR 0233314 |
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