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GENERALIZED (κ˜ ≠ −1, µ˜)-PARACONTACT METRIC MANIFOLDS WITH ξ(µ˜) = 0

Year 2015, Volume: 8 Issue: 1, 77 - 93, 30.04.2015

İrem Küpeli Erken

https://doi.org/10.36890/iejg.592801
Cited By: 1

Abstract


Keywords

Paracontact metric manifold (κ˜; µ˜)-paracontact metric manifold nullity distributions

References

  • [1] Alekseevski, D.V., Cort´es, V., Galaev, A.S. and Leistner, T., Cones over pseudo-Riemannian manifolds and their holonomy, J. Reine Angew. Math. 635 (2009), 23-69.
  • [2] Alekseevski, D.V., Medori, C. and Tomassini, A., Maximally homogeneous para-CR mani- folds, Ann. Glob. Anal. Geom. 30 (2006), 1–27.
  • [3] Bejan, C.L., Almost parahermitian structures on the tangent bundle of an almost para- coHermitian manifold, In: The Proceedings of the Fifth National Seminar of Finsler and Lagrange Spaces (Bra sov, 1988), 105–109, Soc. Stiinte Mat. R. S. Romania, Bucharest, 1989.
  • [4] Buchner, K. and Rosca, R., Vari´etes para-coKählerian ´a champ concirculaire horizontale, C. R. Acad. Sci. Paris 285 (1977), Ser. A, 723–726.
  • [5] Buchner, K. and Rosca, R., Co-isotropic submanifolds of a para-coKa¨hlerian manifold with concicular vector field, J. Geometry 25 (1985), 164–177.
  • [6] Cappelletti Montano, B. and Di Terlizzi, L., Geometric structures associated to a contact metric (κ, µ)-space, Pacific J. Math. 246 no:2 (2010), 257–292.
  • [7] Cappelletti-Montano, B., Kupeli Erken, I. and Murathan, C., Nullity conditions in paracon- tact geometry, Diff. Geom. Appl. 30 (2012), 665–693.
  • [8] Cort´es, V., Mayer, C., Mohaupt, T. and Saueressing, F., Special geometry of Euclidean supersymmetry, 1. Vector multiplets. J. High Energy Phys. (2004) 03:028: 73.
  • [9] Cort´es, V., Lawn, M.A. and Sch¨afer, L., Affine hyperspheres associated to special para-Ka¨hler manifolds, Int. J. Geom. Methods Mod. Phys. 3 (2006), 995–1009.
  • [10] Dacko, P., On almost para-cosymplectic manifolds, Tsukuba J. Math. 28 (2004), 193–213. [11] Kaneyuki, S. and Williams, F. L., Almost paracontact and parahodge structures on manifolds, Nagoya Math. J. 99 (1985), 173–187.
  • [12] Koufogiorgos, T. and Tsichlias, C., On the existence of a new class of contact metric manifolds, Canad. Math. Bull. Vol 43 (2000), 440-447.
  • [13] Koufogiorgos, T. and Tsichlias, C., Generalized (κ, µ)-contact metric manifolds with lgrad κl =constant, J. Geom. 78 (2003), 83-91.
  • [14] Koufogiorgos, T. and Tsichlias, C., Generalized (κ, µ)-contact metric manifolds with ξ(µ) = 0, Tokyo J. Math. Vol 31 (2008), 39-57.
  • [15] Kupeli Erken, I. and Murathan, C., A Complete Study of Three-Dimensional Paracontact (κ, µ, ν)-spaces, Submitted. Available in Arxiv:1305.1511 [math. DG].
  • [16] O’Neill, B., Semi-Riemann Geometry, Academic Press. New York, 1983.
  • [17] Rosca, R. and Vanhecke, L., Su´r une vari´et´e presque paracokähl´erienne munie d’une con- nexion self-orthogonale involutive, Ann. Sti. Univ. “Al. I. Cuza” Ia si 22 (1976), 49–58.
  • [18] Welyczko, J., On basic curvature identities for almost (para)contact metric manifolds. Avail- able in Arxiv: 1209.4731v1 [math. DG].
  • [19] Zamkovoy, S., Canonical connections on paracontact manifolds, Ann. Glob. Anal. Geom. 36 (2009), 37–60.

Year 2015, Volume: 8 Issue: 1, 77 - 93, 30.04.2015

İrem Küpeli Erken

https://doi.org/10.36890/iejg.592801
Cited By: 1

Abstract

References

  • [1] Alekseevski, D.V., Cort´es, V., Galaev, A.S. and Leistner, T., Cones over pseudo-Riemannian manifolds and their holonomy, J. Reine Angew. Math. 635 (2009), 23-69.
  • [2] Alekseevski, D.V., Medori, C. and Tomassini, A., Maximally homogeneous para-CR mani- folds, Ann. Glob. Anal. Geom. 30 (2006), 1–27.
  • [3] Bejan, C.L., Almost parahermitian structures on the tangent bundle of an almost para- coHermitian manifold, In: The Proceedings of the Fifth National Seminar of Finsler and Lagrange Spaces (Bra sov, 1988), 105–109, Soc. Stiinte Mat. R. S. Romania, Bucharest, 1989.
  • [4] Buchner, K. and Rosca, R., Vari´etes para-coKählerian ´a champ concirculaire horizontale, C. R. Acad. Sci. Paris 285 (1977), Ser. A, 723–726.
  • [5] Buchner, K. and Rosca, R., Co-isotropic submanifolds of a para-coKa¨hlerian manifold with concicular vector field, J. Geometry 25 (1985), 164–177.
  • [6] Cappelletti Montano, B. and Di Terlizzi, L., Geometric structures associated to a contact metric (κ, µ)-space, Pacific J. Math. 246 no:2 (2010), 257–292.
  • [7] Cappelletti-Montano, B., Kupeli Erken, I. and Murathan, C., Nullity conditions in paracon- tact geometry, Diff. Geom. Appl. 30 (2012), 665–693.
  • [8] Cort´es, V., Mayer, C., Mohaupt, T. and Saueressing, F., Special geometry of Euclidean supersymmetry, 1. Vector multiplets. J. High Energy Phys. (2004) 03:028: 73.
  • [9] Cort´es, V., Lawn, M.A. and Sch¨afer, L., Affine hyperspheres associated to special para-Ka¨hler manifolds, Int. J. Geom. Methods Mod. Phys. 3 (2006), 995–1009.
  • [10] Dacko, P., On almost para-cosymplectic manifolds, Tsukuba J. Math. 28 (2004), 193–213. [11] Kaneyuki, S. and Williams, F. L., Almost paracontact and parahodge structures on manifolds, Nagoya Math. J. 99 (1985), 173–187.
  • [12] Koufogiorgos, T. and Tsichlias, C., On the existence of a new class of contact metric manifolds, Canad. Math. Bull. Vol 43 (2000), 440-447.
  • [13] Koufogiorgos, T. and Tsichlias, C., Generalized (κ, µ)-contact metric manifolds with lgrad κl =constant, J. Geom. 78 (2003), 83-91.
  • [14] Koufogiorgos, T. and Tsichlias, C., Generalized (κ, µ)-contact metric manifolds with ξ(µ) = 0, Tokyo J. Math. Vol 31 (2008), 39-57.
  • [15] Kupeli Erken, I. and Murathan, C., A Complete Study of Three-Dimensional Paracontact (κ, µ, ν)-spaces, Submitted. Available in Arxiv:1305.1511 [math. DG].
  • [16] O’Neill, B., Semi-Riemann Geometry, Academic Press. New York, 1983.
  • [17] Rosca, R. and Vanhecke, L., Su´r une vari´et´e presque paracokähl´erienne munie d’une con- nexion self-orthogonale involutive, Ann. Sti. Univ. “Al. I. Cuza” Ia si 22 (1976), 49–58.
  • [18] Welyczko, J., On basic curvature identities for almost (para)contact metric manifolds. Avail- able in Arxiv: 1209.4731v1 [math. DG].
  • [19] Zamkovoy, S., Canonical connections on paracontact manifolds, Ann. Glob. Anal. Geom. 36 (2009), 37–60.
There are 18 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

İrem Küpeli Erken

Publication Date April 30, 2015
Published in Issue Year 2015 Volume: 8 Issue: 1

Cite

APA Erken, İ. K. (2015). GENERALIZED (κ˜ ≠ −1, µ˜)-PARACONTACT METRIC MANIFOLDS WITH ξ(µ˜) = 0. International Electronic Journal of Geometry, 8(1), 77-93. https://doi.org/10.36890/iejg.592801
AMA Erken İK. GENERALIZED (κ˜ ≠ −1, µ˜)-PARACONTACT METRIC MANIFOLDS WITH ξ(µ˜) = 0. Int. Electron. J. Geom. April 2015;8(1):77-93. doi:10.36890/iejg.592801
Chicago Erken, İrem Küpeli. “GENERALIZED (κ˜ ≠ −1, µ˜)-PARACONTACT METRIC MANIFOLDS WITH ξ(µ˜) =”. International Electronic Journal of Geometry 8, no. 1 (April 2015): 77-93. https://doi.org/10.36890/iejg.592801.
EndNote Erken İK (April 1, 2015) GENERALIZED (κ˜ ≠ −1, µ˜)-PARACONTACT METRIC MANIFOLDS WITH ξ(µ˜) = 0. International Electronic Journal of Geometry 8 1 77–93.
IEEE İ. K. Erken, “GENERALIZED (κ˜ ≠ −1, µ˜)-PARACONTACT METRIC MANIFOLDS WITH ξ(µ˜) = 0”, Int. Electron. J. Geom., vol. 8, no. 1, pp. 77–93, 2015, doi: 10.36890/iejg.592801.
ISNAD Erken, İrem Küpeli. “GENERALIZED (κ˜ ≠ −1, µ˜)-PARACONTACT METRIC MANIFOLDS WITH ξ(µ˜) =”. International Electronic Journal of Geometry 8/1 (April 2015), 77-93. https://doi.org/10.36890/iejg.592801.
JAMA Erken İK. GENERALIZED (κ˜ ≠ −1, µ˜)-PARACONTACT METRIC MANIFOLDS WITH ξ(µ˜) = 0. Int. Electron. J. Geom. 2015;8:77–93.
MLA Erken, İrem Küpeli. “GENERALIZED (κ˜ ≠ −1, µ˜)-PARACONTACT METRIC MANIFOLDS WITH ξ(µ˜) =”. International Electronic Journal of Geometry, vol. 8, no. 1, 2015, pp. 77-93, doi:10.36890/iejg.592801.
Vancouver Erken İK. GENERALIZED (κ˜ ≠ −1, µ˜)-PARACONTACT METRIC MANIFOLDS WITH ξ(µ˜) = 0. Int. Electron. J. Geom. 2015;8(1):77-93.

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