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2010 | 8 | 4 | 735-753
Tytuł artykułu

Paraquaternionic CR-submanifolds of paraquaternionic Kähler manifolds and semi-Riemannian submersions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we introduce paraquaternionic CR-submanifolds of almost paraquaternionic hermitian manifolds and state some basic results on their differential geometry. We also study a class of semi-Riemannian submersions from paraquaternionic CR-submanifolds of paraquaternionic Kähler manifolds.
Wydawca
Czasopismo
Rocznik
Tom
8
Numer
4
Strony
735-753
Opis fizyczny
Daty
wydano
2010-08-01
online
2010-07-24
Twórcy
autor
  • Department of Mathematics, University of Bucharest, Bucharest, Romania
  • Department of Mathematics and Computer Science, Petroleum-Gas University of Ploieşti, Ploieşti, Romania, gvilcu@mail.upg-ploiesti.ro
Bibliografia
  • [1] Al-Aqeel A., Bejancu A., On normal semi-invariant submanifolds of paraquaternionic Kähler manifolds, Toyama Math. J., 2007, 30, 63–75
  • [2] Alekseevsky D., Cortés V., The twistor spaces of a para-quaternionic Kähler manifold, Osaka J. Math., 2008, 45(1), 215–251
  • [3] Alekseevsky D., Kamishima Y., Quaternionic and para-quaternionic CR structure on (4n+3)-dimensional manifolds, Cent. Eur. J. Math., 2004, 2(5), 732–753 http://dx.doi.org/10.2478/BF02475974[Crossref]
  • [4] Alekseevsky D.V., Marchiafava S., Almost complex submanifolds of quaternionic manifolds, In: Proceedings of the colloquium on differential geometry, Debrecen (Hungary), 25–30 July 2000, Inst. Math. Inform. Debrecen, 2001, 23–38
  • [5] Barros M., Chen B.-Y., Urbano F., Quaternion CR-submanifolds of quaternion manifolds, Kodai Math. J., 1981, 4(3), 399–417 http://dx.doi.org/10.2996/kmj/1138036425[Crossref]
  • [6] Bejancu A., CR submanifolds of a Kaehler manifold I, Proc. Am. Math. Soc., 1978, 69(1), 135–142
  • [7] Bejancu A., Geometry of CR-submanifolds, Mathematics and its Applications (East European Series), 23, D. Reidel Publishing Co., Dordrecht, 1986
  • [8] Bejancu A., Normal semi-invariant submanifolds of paraquaternionic Kähler manifolds, Kuwait J. Sci. Engrg., 2006, 33(2), 33–45
  • [9] Bejancu A., Farran H.R., Foliations and Geometric Structures, Mathematics and Its Applications, 580, Springer, Dordrecht, 2006
  • [10] Blažić N., Paraquaternionic projective spaces and pseudo-Riemannian geometry, Publ. Inst. Math. (Beograd), 1996, 60(74), 101–107
  • [11] Blažić N., Vukmirović S., Solutions of Yang-Mills equations on generalized Hopf bundles, J. Geom. Phys., 2002, 41(1–2), 57–64 [Crossref]
  • [12] Chen B.-Y., Cohomology of CR-submanifolds, Ann. Fac. Sci. Toulouse Math., 1981, 3(2), 167–172 [Crossref]
  • [13] Dancer A.S., Jørgensen H.R., Swann A.F., Metric geometries over the split quaternions, Rend. Sem. Mat. Univ. Politec. Torino, 2005, 63(2), 119–139
  • [14] Falcitelli M., Ianuş S., Pastore A.M., Riemannian Submersions and Related Topics, World Scientific, River Edge, 2004 http://dx.doi.org/10.1142/9789812562333[Crossref]
  • [15] Galicki K., Lawson H.B., Quaternionic reduction and quaternionic orbifolds, Math. Ann., 1988, 282(1), 1–21 http://dx.doi.org/10.1007/BF01457009[Crossref]
  • [16] Garcia-Rio E., Matsushita Y., Vásquez-Lorenzo R., Paraquaternionic Kähler manifolds, Rocky Mountain J. Math., 2001, 31(1), 237–260 http://dx.doi.org/10.1216/rmjm/1008959679[Crossref]
  • [17] Ianuş S., Ionescu A.M., Vîlcu G.E., Foliations on quaternion CR-submanifolds, Houston J. Math., 2008, 34(3), 739–751
  • [18] Ianuş S., Mazzocco R., Vîlcu G.E., Real lightlike hypersurfaces of paraquaternionic Kähler manifolds, Mediterr. J. Math., 2006, 3(3–4), 581–592 [Crossref]
  • [19] Ianuş S., Vîlcu G.E., Some constructions of almost para-hyperhermitian structures on manifolds and tangent bundles, Int. J. Geom. Methods Mod. Phys., 2008, 5(6), 893–903 http://dx.doi.org/10.1142/S0219887808003016[Crossref][WoS]
  • [20] Ionescu A.M., Vîlcu G.E., A note on paraquaternionic manifolds, Missouri J. Math. Sci., 2007, 19(3), 213–218
  • [21] Ivanov S., Zamkovoy S., Parahermitian and paraquaternionic manifolds, Differential Geom. Appl., 2005, 23(2), 205–234 http://dx.doi.org/10.1016/j.difgeo.2005.06.002[Crossref]
  • [22] Kobayashi S., Submersions of CR submanifolds, Tôhoku Math. J., 1987, 39(1), 95–100
  • [23] Libermann P., Sur le problème d’équivalence de certaines structures infinitésimales, Ann. Mat. Pura Appl., 1954, 36, 27–120 http://dx.doi.org/10.1007/BF02412833[Crossref]
  • [24] Marchiafava S., Submanifolds of (para)-quaternionic Kähler manifolds, Note Mat., 2008, 28(suppl.1), 295–316
  • [25] O’Neill B., Semi-Riemannian Geometry. With Applications to Relativity, Pure and Applied Mathematics, 103, Academic Press, New York, 1983
  • [26] Ornea L., CR-submanifolds. A class of examples, Rev. Roumaine Math. Pures Appl., 2006, 51(1), 77–85
  • [27] Vaccaro M., Kaehler and para-Kaehler submanifolds of a para-quaternionic Kaehler manifold, Ph.D. thesis, Università degli Studi di Roma II’ Tor Vergata’, Rome, Italy, 2007
  • [28] Vîlcu G.E., Submanifolds of an Almost Paraquaternionic Kähler Product Manifold, Int. Math. Forum, 2007, 2(15), 735–746
  • [29] Vukmirovic S., Paraquaternionic reduction, preprint available at http://arxiv.org/abs/math/0304424
  • [30] Wu H., On the de Rham decomposition theorem, Illinois J. Math., 1964, 8, 291–311
  • [31] Yano K., Kon M., CR Submanifolds of Kaehlerian and Sasakian Manifolds, Progress in Mathematics, 30, Birkhäuser, Boston, 1983
  • [32] Zamkovoy S., Geometry of paraquaternionic Kähler manifolds with torsion, J. Geom. Phys., 2006, 57(1), 69–87 http://dx.doi.org/10.1016/j.geomphys.2006.02.003[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-010-0048-x
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