Natural diagonal Riemannian almost product and para-Hermitian cotangent bundles

Simona-Luiza Druţă-Romaniuc

Czechoslovak Mathematical Journal (2012)

  • Volume: 62, Issue: 4, page 937-949
  • ISSN: 0011-4642

Abstract

top
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.

How to cite

top

Druţă-Romaniuc, Simona-Luiza. "Natural diagonal Riemannian almost product and para-Hermitian cotangent bundles." Czechoslovak Mathematical Journal 62.4 (2012): 937-949. <http://eudml.org/doc/247207>.

@article{Druţă2012,
abstract = {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.},
author = {Druţă-Romaniuc, Simona-Luiza},
journal = {Czechoslovak Mathematical Journal},
keywords = {natural lift; cotangent bundle; almost product structure; para-Hermitian structure; para-Kähler structure; cotangent bundle; almost product structure; para-Hermitian structure; para-Kähler structure},
language = {eng},
number = {4},
pages = {937-949},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Natural diagonal Riemannian almost product and para-Hermitian cotangent bundles},
url = {http://eudml.org/doc/247207},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Druţă-Romaniuc, Simona-Luiza
TI - Natural diagonal Riemannian almost product and para-Hermitian cotangent bundles
JO - Czechoslovak Mathematical Journal
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 4
SP - 937
EP - 949
AB - 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.
LA - eng
KW - natural lift; cotangent bundle; almost product structure; para-Hermitian structure; para-Kähler structure; cotangent bundle; almost product structure; para-Hermitian structure; para-Kähler structure
UR - http://eudml.org/doc/247207
ER -

References

top
  1. Alekseevsky, D. V., Medori, C., Tomassini, A., 10.1070/RM2009v064n01ABEH004591, Russ. Math. Surv. 64 (2009), 1-43. (2009) Zbl1179.53050MR2503094DOI10.1070/RM2009v064n01ABEH004591
  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. (2000) MR1814928
  3. Bejan, C., A classification of the almost parahermitian manifolds, Differential Geometry and Its Application Proc. Conf. Dubrovnik/Yougosl. 1988 (1989), 23-27. (1989) Zbl0683.53034MR1040052
  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. (1989) 
  5. Bejan, C., Ornea, L., 10.1155/S0161171298000854, Int. J. Math. Math. Sci. 21 (1998), 613-618. (1998) Zbl0906.53016MR1620323DOI10.1155/S0161171298000854
  6. Cruceanu, V., Selected Papers, Editura PIM Iaşi (2006). (2006) 
  7. Druţă, S. L., Cotangent bundles with general natural Kähler structures, Rev. Roum. Math. Pures Appl. 54 (2009), 13-23. (2009) Zbl1212.53041MR2503281
  8. Gadea, P. M., Masqué, J. M., Classification of almost para-Hermitian manifolds, Rend. Mat. Appl. 11 (1991), 377-396. (1991) MR1122346
  9. Farran, H. K., Zanoun, M. S., On hyperbolic Hermite manifolds, Publ. Inst. Math., Nouv. Sér. 46 (1989), 173-182. (1989) Zbl0702.53026MR1060071
  10. Heydari, A., Peyghan, E., A characterization of the infinitesimal conformal transformations on tangent bundles, Bull. Iran. Math. Soc. 34 (2008), 59-70. (2008) Zbl1176.53027MR2477994
  11. Ivanov, S., Zamkovoy, S., 10.1016/j.difgeo.2005.06.002, Differ. Geom. Appl. 23 (2005), 205-234. (2005) Zbl1115.53022MR2158044DOI10.1016/j.difgeo.2005.06.002
  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. (1994) MR1344006
  13. Kolář, I., Michor, P. W., Slovák, J., Natural Operations in Differential Geometry, Springer Berlin (1993). (1993) MR1202431
  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. (1988) Zbl0656.53021MR0974641
  15. Luczyszyn, D., Olszak, Z., 10.4134/JKMS.2008.45.4.953, J. Korean Math. Soc. 45 (2008), 953-963. (2008) Zbl1154.53017MR2422720DOI10.4134/JKMS.2008.45.4.953
  16. Mekerov, D., 10.1007/s00022-008-2084-2, J. Geom. 89 (2008), 119-129. (2008) Zbl1166.53018MR2457026DOI10.1007/s00022-008-2084-2
  17. Mihai, I., Nicolau, C., Almost product structures on the tangent bundle of an almost paracontact manifold, Demonstr. Math. 15 (1982), 1045-1058. (1982) Zbl0522.53030MR0705829
  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. (1977) Zbl0363.53016MR0500673
  19. Munteanu, M.-I., CR-structures on the unit cotangent bundle and Bochner type tensor, An. Ştiinţ. Univ. Al. I. Cuza Iaşi A, Ser. Nouǎ, Mat. 44 (1998), 125-136. (1998) Zbl1011.53028MR1719809
  20. Naveira, A. M., A classification of Riemannian almost product manifolds, Rend. Math. Appl. VII. Ser. 3 (1983), 577-592. (1983) Zbl0538.53045MR0743400
  21. Oproiu, V., Papaghiuc, N., A pseudo-Riemannian structure on the cotangent bundle, An. Ştiinţ. Univ. Al. I. Cuza Iaşi, Ser. Nouǎ Mat. 36 (1990), 265-276. (1990) Zbl0758.53036MR1157451
  22. Oproiu, V., Papaghiuc, N., Mitric, G., Some classes of parahermitian structures on cotangent bundles, An. Ştiinţ. Univ. Al. I. Cuza Iaşi, Ser. Nouǎ Mat. 43 (1996), 7-22. (1996) Zbl0974.53504MR1679101
  23. Oproiu, V., Poroşniuc, D. D., A class of Kähler Einstein structures on the cotangent bundle, Publ. Math. 66 (2005), 457-478. (2005) Zbl1082.53029MR2137782
  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. (2010) Zbl1193.53040MR2577131
  25. Staikova, M. T., Gribachev, K. I., Canonical connections and conformal invariants on Riemannian almost-product manifolds, Serdica 18 (1992), 150-161. (1992) MR1224633
  26. Yano, K., Differential Geometry on a Complex and Almost Complex Spaces, Pergamon Press Oxford-London-New York-Paris-Frankfurt (1965). (1965) 
  27. Yano, K., Ishihara, S., Tangent and Cotangent Bundles, Marcel Dekker Inc. New York (1973). (1973) Zbl0262.53024MR0350650

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.