Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
Einstein manifold; quasi-Einstein manifold; generalized quasi-Einstein manifold; mixed generalized quasi-Einstein manifold; super quasi-Einstein manifold; warped product
Einstein manifold; quasi-Einstein manifold; generalized quasi-Einstein manifold; mixed generalized quasi-Einstein manifold; super quasi-Einstein manifold; warped product
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.
References:
[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. MR 3674593 | Zbl 1365.53021
[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
[3] Besse, A. L.: Einstein Manifolds. Springer-Verlag, New York, 1987. MR 0867684 | Zbl 0613.53001
[4] Bhattacharya,, A., De, T.: On mixed generalized quasi Einstein manifolds. Differ. Geom. Dyn. Syst. 9 (2007), 40–46, (electronic). MR 2308620
[5] Bishop, R. L., O’Neill, B.: Geometry of slant Submanifolds. Trans. Amer. Math. Soc. 145 (1969), 1–49. MR 0251664
[6] Chaki, M. C.: On super quasi-Einstein manifolds. Publ. Math. Debrecen 64 (2004), 481–488. MR 2059079 | Zbl 1093.53045
[7] Chen, B. Y.: Some new obstructions to minimal and Lagrangian isometric immersions. Japan. J. Math. (N.S.) 26 (2000), 105–127. DOI 10.4099/math1924.26.105 | MR 1771434 | Zbl 1026.53009
[8] De, U. C., Ghosh, G. C.: On generalized quasi-Einstein manifolds. Kyungpook Math. J. 44 (2004), 607–615. MR 2108466 | Zbl 1076.53509
[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
[10] Dumitru, D.: On Einstein spaces of odd dimension. Bul. Transilv. Univ. Brasov Ser. B (N.S.) 14, suppl. 49 (2007), 95–97. MR 2446794 | Zbl 1195.53058
[11] Formella, S., Mikeš, J.: Geodesic mappings of Einstein spaces. Ann. Sci. Stetinenses 9 (1994), 31–40.
[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
[13] Hinterleitner, I., Mikeš, J.: Geodesic mappings and Einstein spaces. In: Geometric methods in physics, Trends in Mathematics, Birkhäuser, Basel, 2013, 331–335. MR 3364052 | Zbl 1268.53049
[14] Kagan, V. F.: Subprojective Spaces. Fizmatgiz, Moscow, 1961.
[15] O'Neill, B.: Semi-Riemannian Geometry wih Applications to Relativity.
[16] Mikeš, J.: Geodesic mapping of affine-connected and Riemannian spaces. J. Math. Sci. 78, 3 (1996), 311–333. DOI 10.1007/BF02365193 | MR 1384327
[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
[18] Mikeš, J.: Geodesic mappings of Einstein spaces. Math. Notes 28 (1981), 922–923. DOI 10.1007/BF01709156 | MR 0603226 | Zbl 0461.53013
[19] Mikeš, J.: Differential geometry of special mappings. Palacky Univ. Press, Olomouc, 2015. MR 3442960 | Zbl 1337.53001
[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
Search
Partner of
