Title:
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Natural diagonal Riemannian almost product and para-Hermitian cotangent bundles (English) |
Author:
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Druţă-Romaniuc, Simona-Luiza |
Language:
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English |
Journal:
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Czechoslovak Mathematical Journal |
ISSN:
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0011-4642 (print) |
ISSN:
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1572-9141 (online) |
Volume:
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62 |
Issue:
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4 |
Year:
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2012 |
Pages:
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937-949 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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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:
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natural lift |
Keyword:
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cotangent bundle |
Keyword:
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almost product structure |
Keyword:
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para-Hermitian structure |
Keyword:
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para-Kähler structure |
MSC:
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53C05 |
MSC:
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53C15 |
MSC:
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53C55 |
idZBL:
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Zbl 1274.53040 |
idMR:
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MR3010249 |
DOI:
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10.1007/s10587-012-0075-9 |
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Date available:
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2012-11-10T21:33:04Z |
Last updated:
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2020-07-03 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/143037 |
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Reference:
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[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 |
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