Previous |  Up |  Next

Article

Title: Natural diagonal Riemannian almost product and para-Hermitian cotangent bundles (English)
Author: Druţă-Romaniuc, Simona-Luiza
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 62
Issue: 4
Year: 2012
Pages: 937-949
Summary lang: English
.
Category: math
.
Summary: We obtain the natural diagonal almost product and locally product structures on the total space of the cotangent bundle of a Riemannian manifold. Studying the compatibility and the anti-compatibility relations between the determined structures and a natural diagonal metric, we find the Riemannian almost product (locally product) and the (almost) para-Hermitian cotangent bundles of natural diagonal lift type. Finally, we prove the characterization theorem for the natural diagonal (almost) para-Kählerian structures on the total space of the cotangent bundle. (English)
Keyword: natural lift
Keyword: cotangent bundle
Keyword: almost product structure
Keyword: para-Hermitian structure
Keyword: para-Kähler structure
MSC: 53C05
MSC: 53C15
MSC: 53C55
idZBL: Zbl 1274.53040
idMR: MR3010249
DOI: 10.1007/s10587-012-0075-9
.
Date available: 2012-11-10T21:33:04Z
Last updated: 2020-07-03
Stable URL: http://hdl.handle.net/10338.dmlcz/143037
.
Reference: [1] Alekseevsky, D. V., Medori, C., Tomassini, A.: Homogeneous para-Kähler Einstein manifolds.Russ. Math. Surv. 64 (2009), 1-43. Zbl 1179.53050, MR 2503094, 10.1070/RM2009v064n01ABEH004591
Reference: [2] Anastasiei, M.: Some Riemannian almost product structures on tangent manifold. Proceedings of the 11th National Conference on Finsler, Lagrange and Hamilton Geometry (Craiova, 2000).Algebras Groups Geom. 17 (2000), 253-262. MR 1814928
Reference: [3] Bejan, C.: A classification of the almost parahermitian manifolds.Differential Geometry and Its Application Proc. Conf. Dubrovnik/Yougosl. 1988 (1989), 23-27. Zbl 0683.53034, MR 1040052
Reference: [4] Bejan, C.: Almost parahermitian structures on the tangent bundle of an almost para-co-Hermitian manifold.Finsler and Lagrange Spaces, Proc. 5th Natl. Semin., Braşov, 1988 Soc. Ştiinţe Math. R. S. România Bucharest (1989), 105-109.
Reference: [5] Bejan, C., Ornea, L.: An example of an almost hyperbolic Hermitian manifold.Int. J. Math. Math. Sci. 21 (1998), 613-618. Zbl 0906.53016, MR 1620323, 10.1155/S0161171298000854
Reference: [6] Cruceanu, V.: Selected Papers.Editura PIM Iaşi (2006).
Reference: [7] Druţă, S. L.: Cotangent bundles with general natural Kähler structures.Rev. Roum. Math. Pures Appl. 54 (2009), 13-23. Zbl 1212.53041, MR 2503281
Reference: [8] Gadea, P. M., Masqué, J. M.: Classification of almost para-Hermitian manifolds.Rend. Mat. Appl. 11 (1991), 377-396. MR 1122346
Reference: [9] Farran, H. K., Zanoun, M. S.: On hyperbolic Hermite manifolds.Publ. Inst. Math., Nouv. Sér. 46 (1989), 173-182. Zbl 0702.53026, MR 1060071
Reference: [10] Heydari, A., Peyghan, E.: A characterization of the infinitesimal conformal transformations on tangent bundles.Bull. Iran. Math. Soc. 34 (2008), 59-70. Zbl 1176.53027, MR 2477994
Reference: [11] Ivanov, S., Zamkovoy, S.: Para-Hermitian and paraquaternionic manifolds.Differ. Geom. Appl. 23 (2005), 205-234. Zbl 1115.53022, MR 2158044, 10.1016/j.difgeo.2005.06.002
Reference: [12] Kolář, I.: On cotangent bundles of some natural bundles. Geometry and physics. Proc. of the Winter School of Geometry and Physics (Zdíkov, 1993).Rend. Circ. Mat. Palermo Suppl. 37 (1994), 115-120. MR 1344006
Reference: [13] Kolář, I., Michor, P. W., Slovák, J.: Natural Operations in Differential Geometry.Springer Berlin (1993). MR 1202431
Reference: [14] Kowalski, O., Sekizawa, M.: Natural transformations of Riemannian metrics on manifolds to metrics on tangent bundles---a classification.Bull. Tokyo Gakugei Univ., Sect. IV 40 (1988), 1-29. Zbl 0656.53021, MR 0974641
Reference: [15] Luczyszyn, D., Olszak, Z.: On paraholomorphically pseudosymmetric para-Kählerian manifolds.J. Korean Math. Soc. 45 (2008), 953-963. Zbl 1154.53017, MR 2422720, 10.4134/JKMS.2008.45.4.953
Reference: [16] Mekerov, D.: On Riemannian almost product manifolds with nonintegrable structure.J. Geom. 89 (2008), 119-129. Zbl 1166.53018, MR 2457026, 10.1007/s00022-008-2084-2
Reference: [17] Mihai, I., Nicolau, C.: Almost product structures on the tangent bundle of an almost paracontact manifold.Demonstr. Math. 15 (1982), 1045-1058. Zbl 0522.53030, MR 0705829
Reference: [18] Mok, K.-P., Patterson, E. M., Wong, Y.-C.: Structure of symmetric tensors of type (0,2) and tensors of type (1,1) on the tangent bundle.Trans. Am. Math. Soc. 234 (1977), 253-278. Zbl 0363.53016, MR 0500673
Reference: [19] Munteanu, M.-I.: CR-structures on the unit cotangent bundle and Bochner type tensor.An. Ştiinţ. Univ. Al. I. Cuza Iaşi A, Ser. Nou\v a, Mat. 44 (1998), 125-136. Zbl 1011.53028, MR 1719809
Reference: [20] Naveira, A. M.: A classification of Riemannian almost product manifolds.Rend. Math. Appl. VII. Ser. 3 (1983), 577-592. Zbl 0538.53045, MR 0743400
Reference: [21] Oproiu, V., Papaghiuc, N.: A pseudo-Riemannian structure on the cotangent bundle.An. Ştiinţ. Univ. Al. I. Cuza Iaşi, Ser. Nou\v a Mat. 36 (1990), 265-276. Zbl 0758.53036, MR 1157451
Reference: [22] Oproiu, V., Papaghiuc, N., Mitric, G.: Some classes of parahermitian structures on cotangent bundles.An. Ştiinţ. Univ. Al. I. Cuza Iaşi, Ser. Nou\v a Mat. 43 (1996), 7-22. Zbl 0974.53504, MR 1679101
Reference: [23] Oproiu, V., Poroşniuc, D. D.: A class of Kähler Einstein structures on the cotangent bundle.Publ. Math. 66 (2005), 457-478. Zbl 1082.53029, MR 2137782
Reference: [24] Peyghan, E., Heydari, A.: A class of locally symmetric para-Kähler Einstein structures on the cotangent bundle.Int. Math. Forum 5 (2010), 145-153. Zbl 1193.53040, MR 2577131
Reference: [25] Staikova, M. T., Gribachev, K. I.: Canonical connections and conformal invariants on Riemannian almost-product manifolds.Serdica 18 (1992), 150-161. MR 1224633
Reference: [26] Yano, K.: Differential Geometry on a Complex and Almost Complex Spaces.Pergamon Press Oxford-London-New York-Paris-Frankfurt (1965).
Reference: [27] Yano, K., Ishihara, S.: Tangent and Cotangent Bundles.Marcel Dekker Inc. New York (1973). Zbl 0262.53024, MR 0350650
.

Files

Files Size Format View
CzechMathJ_62-2012-4_6.pdf 271.7Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo