| Title:
|
Characterization on Mixed Generalized Quasi-Einstein Manifold (English) |
| Author:
|
Pahan, Sampa |
| Author:
|
Pal, Buddhadev |
| Author:
|
BHATTACHARYYA, Arindam |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
55 |
| Issue:
|
2 |
| Year:
|
2016 |
| Pages:
|
143-155 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the present paper we study characterizations of odd and even dimensional mixed generalized quasi-Einstein manifold. Next we prove that a mixed generalized quasi-Einstein manifold is a generalized quasi-Einstein manifold under a certain condition. Then we obtain three and four dimensional examples of mixed generalized quasi-Einstein manifold to ensure the existence of such manifold. Finally we establish the examples of warped product on mixed generalized quasi-Einstein manifold. (English) |
| Keyword:
|
Einstein manifold |
| Keyword:
|
quasi-Einstein manifold |
| Keyword:
|
generalized quasi-Einstein manifold |
| Keyword:
|
mixed generalized quasi-Einstein manifold |
| Keyword:
|
super quasi-Einstein manifold |
| Keyword:
|
warped product |
| MSC:
|
53C25 |
| idZBL:
|
Zbl 1365.53047 |
| . |
| Date available:
|
2017-03-16T12:53:18Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146067 |
| . |
| Reference:
|
[1] Baishya, K. K., Peška, P.: On the example of almost pseudo-Z-symmetric manifolds.. Acta Univ. Palacki. Olomuc., Fac. Rer. Nat., Math. 55, 1 (2016), 5–40. Zbl 1365.53021, MR 3674593 |
| Reference:
|
[2] Bejan, C. L.: Characterization of quasi Einstein manifolds.. An. Stiint. Univ.“Al. I. Cuza” Iasi Mat. (N.S.) 53, suppl. 1 (2007), 67–72. MR 2522383 |
| Reference:
|
[3] Besse, A. L.: Einstein Manifolds.. Springer-Verlag, New York, 1987. Zbl 0613.53001, MR 0867684 |
| Reference:
|
[4] Bhattacharya,, A., De, T.: On mixed generalized quasi Einstein manifolds.. Differ. Geom. Dyn. Syst. 9 (2007), 40–46, (electronic). MR 2308620 |
| Reference:
|
[5] Bishop, R. L., O’Neill, B.: Geometry of slant Submanifolds.. Trans. Amer. Math. Soc. 145 (1969), 1–49. MR 0251664 |
| Reference:
|
[6] Chaki, M. C.: On super quasi-Einstein manifolds.. Publ. Math. Debrecen 64 (2004), 481–488. Zbl 1093.53045, MR 2059079 |
| Reference:
|
[7] Chen, B. Y.: Some new obstructions to minimal and Lagrangian isometric immersions.. Japan. J. Math. (N.S.) 26 (2000), 105–127. Zbl 1026.53009, MR 1771434, 10.4099/math1924.26.105 |
| Reference:
|
[8] De, U. C., Ghosh, G. C.: On generalized quasi-Einstein manifolds.. Kyungpook Math. J. 44 (2004), 607–615. Zbl 1076.53509, MR 2108466 |
| Reference:
|
[9] Deszcz, R., Glogowska, M., Holtos, M., Senturk, Z.: On certain quasi-Einstein semisymmetric hypersurfaces.. Annl. Univ. Sci. Budapest. Eötvös Sect. Math 41 (1998), 151–164. MR 1691925 |
| Reference:
|
[10] Dumitru, D.: On Einstein spaces of odd dimension.. Bul. Transilv. Univ. Brasov Ser. B (N.S.) 14, suppl. 49 (2007), 95–97. Zbl 1195.53058, MR 2446794 |
| Reference:
|
[11] Formella, S., Mikeš, J.: Geodesic mappings of Einstein spaces.. Ann. Sci. Stetinenses 9 (1994), 31–40. |
| Reference:
|
[12] Halder, K., Pal, B., Bhattacharya, A., De, T.: Characterization of super quasi Einstein manifolds.. An. Stiint. Univ.“Al. I. Cuza” Iasi Mat. (N.S.) 60, 1 (2014), 99–108. MR 3252460 |
| Reference:
|
[13] Hinterleitner, I., Mikeš, J.: Geodesic mappings and Einstein spaces.. In: Geometric methods in physics, Trends in Mathematics, Birkhäuser, Basel, 2013, 331–335. Zbl 1268.53049, MR 3364052 |
| Reference:
|
[14] Kagan, V. F.: Subprojective Spaces.. Fizmatgiz, Moscow, 1961. |
| Reference:
|
[15] O'Neill, B.: Semi-Riemannian Geometry wih Applications to Relativity. |
| Reference:
|
[16] Mikeš, J.: Geodesic mapping of affine-connected and Riemannian spaces.. J. Math. Sci. 78, 3 (1996), 311–333. MR 1384327, 10.1007/BF02365193 |
| Reference:
|
[17] Mikeš, J.: Geodesic mappings of special Riemannian spaces.. In: Coll. Math. Soc. J. Bolyai 46, Topics in Diff. Geom. Debrecen (Hungary), 1984, Amsterdam, 1988, 793–813. MR 0933875 |
| Reference:
|
[18] Mikeš, J.: Geodesic mappings of Einstein spaces.. Math. Notes 28 (1981), 922–923. Zbl 0461.53013, MR 0603226, 10.1007/BF01709156 |
| Reference:
|
[19] Mikeš, J.: Differential geometry of special mappings.. Palacky Univ. Press, Olomouc, 2015. Zbl 1337.53001, MR 3442960 |
| Reference:
|
[20] Singer, I. M., Thorpe, J. A.: The curvature of 4-dimensional Einstein spaces. In: Global Analysis (Papers in honor of K. Kodaira, Princeton Univ. Press, Princeton, 1969, 355–365. Zbl 0199.25401 |
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