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RICCI SOLITONS IN 3-DIMENSIONAL NORMAL ALMOST PARACONTACT METRIC MANIFOLDS

Year 2015, Volume: 8 Issue: 2, 34 - 45, 30.10.2015
https://doi.org/10.36890/iejg.592276

Abstract


References

  • [1] Akbar, M.M., Woolgar, E., Ricci solitons and Einstein-scalar field theory , Class. Quantum Grav., 26, 055015 (14pp), 2009, doi:10.1088/0264-9381/26/5/055015.
  • [2] Alekseevski, D. V., Cort´es, V., Galaev, A. S., Leistner, T. , Cones over pseudo-Riemannian manifolds and their holonomy, J. Reine Angew. Math., 635 (2009), 23-69.
  • [3] Alekseevski, D. V., Medori, C., Tomassini, A., Maximally homogeneous para-CR manifolds, Ann. Global Anal. Geom., 30 (2006), 1-27.
  • [4] Brozos-Vazquez, M., Calvaruso, G., Garcia-Rio, E., Gavino-Fernandez, S., Three-dimensional Lorentzian Homogenous Ricci Solitons, Israel J Math 188 (2012), 385-403.
  • [5] Case, J. S., Singularity theorems and the Lorentzian splitting theorem for the Bakry Emery Ricci Tensor, Journal of Geometry and Physics 60 (2010), 477-490.
  • [6] Chow, B., Knopf, D., The Ricci flow: an introduction, volume 110 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, 2004.
  • [7] Cort´es, V., Mayer, C., Mohaupt, T., Saueressing, F., Special geometry of Euclidean super- symmetry 1. Vector multiplets, J. High Energy Phys., 0403 (2004), 028, 73 pp.
  • [8] Cort´es, V., Lawn, M. A., Sch¨afer, L., Affine hyperspheres associated to special para-Ka¨hler manifolds, Int. J. Geom. Methods Mod. Phys., 3 (2006), 995-1009.
  • [9] Dacko, P., On almost paracosymplectic manifolds, Tsukuba J. Math. 28 (2004), no.1, 193-213.
  • [10] Das, S., Prabhu, K., Sayan K., Int. J. Geom. Methods Mod. Phys. 07, 837 (2010). DOI:10.1142/S0219887810004579.
  • [11] De, U.C., Turan, M., Yıldız, A., De, A., Ricci solitons and gradient Ricci solitons on 3- dimensional normal almost contact metric manifolds, Publ. Math. Debrecen, Ref. no.: 4947, (2012), 1-16.
  • [12] Erdem, S., On almost (para)contact (hyperbolic) metric manifolds and harmonicity of (φ, φ′)- holomorphic maps between them, Houston J. Math., 28 (2002), 21-45.
  • [13] Erdem, S., On almost (para)contact (hyperbolic) metric manifolds and harmonicity of (φ, φ′)- holomorphic maps between them, Houston J. Math., 28 (2002), 21-45.
  • [14] Friedan, D., Nonlinear models in 2 + ε dimensions, Ann. Phys., 163(2), 318-419, 1985.
  • [15] Ghosh, A., Kenmotsu 3-metric as a Ricci soliton, Chaos, Solitons & Fractals 44 (8), 2011, 647–650.
  • [16] Ghosh, A., Sharma, R., Cho, J.T., Contact metric manifolds with η-parallel torsion tensor, Annals of Global Analysis and Geometry, 34, 287-299, 2008.
  • [17] Hamilton, R. S., Three-manifolds with positive Ricci curvature. J. Di . Geo., 17:255-306,1982
  • [18] Hamilton, R. S., The Ricci flow on surfaces, Mathematics and general relativity (SantaCruz, CA,1986), Contemp. Math. 71, A.M.S., 237-262, 1988.
  • [19] Ivey, T., Ricci solitons on compact 3-manifolds, Differential Geo. Appl. 3, 301-307, 1993.
  • [20] Kaneyuki, S., Konzai, M., Paracomplex structure and affine symmetric spaces, Tokyo J. Math., 8 (1985), 301-308.
  • [21] Kaneyuki, S., Willams, F. L., Almost paracontact and parahodge structure on manifolds, Nagoya Math. J., 99, 173-187, 1985.
  • [22] Kholodenko, A. L., Towards physically motivated proofs of the Poincar´e and the geometriza- tion conjectures, Journal of Geometry and Physics 58, 259–290, 2008.
  • [23] Nagaraja, H.G., Premalatha, C.R., Ricci solitons in Kenmotsu manifolds, Journal of Mathe- matical Analysis, vol. 3, no. 2, pp. 18–24, 2012.
  • [24] Payne, T. L., The existence of soliton metrics for nilponent Lie Groups, Geometriae Dedicate 145 (2010), 71-88.
  • [25] Perelman, G., The entropy formula for the Ricci flow and its geometric applications,ArXiv:math.DG/0211159
  • [26] Sharma, R., Certain Results on K-Contact and (k, µ)-Contact Manifolds, J. Geom. 89 (2008), 138-147.
  • [27] Sharma, R., Ghosh, A., Sasakian 3-manifolds as a Ricci soliton represents the Heisenberg group, International Journal of Geometric Methods in Modern Physics, 2011 08:01, 149-154
  • [28] Tripathi, M.M., Ricci solitons in contact metric manifolds, arXiv:0801.4222, 2008.
  • [29] Turan, M., De, U.C., Yıldız, A.,Ricci solitons and gradient Ricci solitons in three- dimensional trans-Sasakian manifolds, Filomat, Volume 26, Issue 2, Pages: 363-370, 2012, doi:10.2298/FIL1202363T.
  • [30] Willmore, T.J., Differential Geometry, Clarendon Press, Oxford, 1958.
  • [31] Woolgar, E., Some applications of Ricci flow in physics, Canadian Journal of Physics, 2008, 86(4): 645-651, 10.1139/p07-146.
  • [32] Welyczko, J., Legendre curves in 3-dimensional Normal almost paracontact metric manifolds, Result. Mth. 54 (2009), 377-387.
  • [33] Welyczko, J., Slant curves in 3-dimensional normal almost paracontact metric manifolds, Mediterr. J. Math. 11 (2014), no. 3, 965978.
  • [34] Zamkovoy, S.,Canonical connection on paracontact manifolds, Ann. Glob. Anal. Geo., 36 (2009), 37-60.
Year 2015, Volume: 8 Issue: 2, 34 - 45, 30.10.2015
https://doi.org/10.36890/iejg.592276

Abstract

References

  • [1] Akbar, M.M., Woolgar, E., Ricci solitons and Einstein-scalar field theory , Class. Quantum Grav., 26, 055015 (14pp), 2009, doi:10.1088/0264-9381/26/5/055015.
  • [2] Alekseevski, D. V., Cort´es, V., Galaev, A. S., Leistner, T. , Cones over pseudo-Riemannian manifolds and their holonomy, J. Reine Angew. Math., 635 (2009), 23-69.
  • [3] Alekseevski, D. V., Medori, C., Tomassini, A., Maximally homogeneous para-CR manifolds, Ann. Global Anal. Geom., 30 (2006), 1-27.
  • [4] Brozos-Vazquez, M., Calvaruso, G., Garcia-Rio, E., Gavino-Fernandez, S., Three-dimensional Lorentzian Homogenous Ricci Solitons, Israel J Math 188 (2012), 385-403.
  • [5] Case, J. S., Singularity theorems and the Lorentzian splitting theorem for the Bakry Emery Ricci Tensor, Journal of Geometry and Physics 60 (2010), 477-490.
  • [6] Chow, B., Knopf, D., The Ricci flow: an introduction, volume 110 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, 2004.
  • [7] Cort´es, V., Mayer, C., Mohaupt, T., Saueressing, F., Special geometry of Euclidean super- symmetry 1. Vector multiplets, J. High Energy Phys., 0403 (2004), 028, 73 pp.
  • [8] Cort´es, V., Lawn, M. A., Sch¨afer, L., Affine hyperspheres associated to special para-Ka¨hler manifolds, Int. J. Geom. Methods Mod. Phys., 3 (2006), 995-1009.
  • [9] Dacko, P., On almost paracosymplectic manifolds, Tsukuba J. Math. 28 (2004), no.1, 193-213.
  • [10] Das, S., Prabhu, K., Sayan K., Int. J. Geom. Methods Mod. Phys. 07, 837 (2010). DOI:10.1142/S0219887810004579.
  • [11] De, U.C., Turan, M., Yıldız, A., De, A., Ricci solitons and gradient Ricci solitons on 3- dimensional normal almost contact metric manifolds, Publ. Math. Debrecen, Ref. no.: 4947, (2012), 1-16.
  • [12] Erdem, S., On almost (para)contact (hyperbolic) metric manifolds and harmonicity of (φ, φ′)- holomorphic maps between them, Houston J. Math., 28 (2002), 21-45.
  • [13] Erdem, S., On almost (para)contact (hyperbolic) metric manifolds and harmonicity of (φ, φ′)- holomorphic maps between them, Houston J. Math., 28 (2002), 21-45.
  • [14] Friedan, D., Nonlinear models in 2 + ε dimensions, Ann. Phys., 163(2), 318-419, 1985.
  • [15] Ghosh, A., Kenmotsu 3-metric as a Ricci soliton, Chaos, Solitons & Fractals 44 (8), 2011, 647–650.
  • [16] Ghosh, A., Sharma, R., Cho, J.T., Contact metric manifolds with η-parallel torsion tensor, Annals of Global Analysis and Geometry, 34, 287-299, 2008.
  • [17] Hamilton, R. S., Three-manifolds with positive Ricci curvature. J. Di . Geo., 17:255-306,1982
  • [18] Hamilton, R. S., The Ricci flow on surfaces, Mathematics and general relativity (SantaCruz, CA,1986), Contemp. Math. 71, A.M.S., 237-262, 1988.
  • [19] Ivey, T., Ricci solitons on compact 3-manifolds, Differential Geo. Appl. 3, 301-307, 1993.
  • [20] Kaneyuki, S., Konzai, M., Paracomplex structure and affine symmetric spaces, Tokyo J. Math., 8 (1985), 301-308.
  • [21] Kaneyuki, S., Willams, F. L., Almost paracontact and parahodge structure on manifolds, Nagoya Math. J., 99, 173-187, 1985.
  • [22] Kholodenko, A. L., Towards physically motivated proofs of the Poincar´e and the geometriza- tion conjectures, Journal of Geometry and Physics 58, 259–290, 2008.
  • [23] Nagaraja, H.G., Premalatha, C.R., Ricci solitons in Kenmotsu manifolds, Journal of Mathe- matical Analysis, vol. 3, no. 2, pp. 18–24, 2012.
  • [24] Payne, T. L., The existence of soliton metrics for nilponent Lie Groups, Geometriae Dedicate 145 (2010), 71-88.
  • [25] Perelman, G., The entropy formula for the Ricci flow and its geometric applications,ArXiv:math.DG/0211159
  • [26] Sharma, R., Certain Results on K-Contact and (k, µ)-Contact Manifolds, J. Geom. 89 (2008), 138-147.
  • [27] Sharma, R., Ghosh, A., Sasakian 3-manifolds as a Ricci soliton represents the Heisenberg group, International Journal of Geometric Methods in Modern Physics, 2011 08:01, 149-154
  • [28] Tripathi, M.M., Ricci solitons in contact metric manifolds, arXiv:0801.4222, 2008.
  • [29] Turan, M., De, U.C., Yıldız, A.,Ricci solitons and gradient Ricci solitons in three- dimensional trans-Sasakian manifolds, Filomat, Volume 26, Issue 2, Pages: 363-370, 2012, doi:10.2298/FIL1202363T.
  • [30] Willmore, T.J., Differential Geometry, Clarendon Press, Oxford, 1958.
  • [31] Woolgar, E., Some applications of Ricci flow in physics, Canadian Journal of Physics, 2008, 86(4): 645-651, 10.1139/p07-146.
  • [32] Welyczko, J., Legendre curves in 3-dimensional Normal almost paracontact metric manifolds, Result. Mth. 54 (2009), 377-387.
  • [33] Welyczko, J., Slant curves in 3-dimensional normal almost paracontact metric manifolds, Mediterr. J. Math. 11 (2014), no. 3, 965978.
  • [34] Zamkovoy, S.,Canonical connection on paracontact manifolds, Ann. Glob. Anal. Geo., 36 (2009), 37-60.
There are 34 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Selcen Yüksel Perktaş This is me

Sadik Keleş

Publication Date October 30, 2015
Published in Issue Year 2015 Volume: 8 Issue: 2

Cite

APA Perktaş, S. Y., & Keleş, S. (2015). RICCI SOLITONS IN 3-DIMENSIONAL NORMAL ALMOST PARACONTACT METRIC MANIFOLDS. International Electronic Journal of Geometry, 8(2), 34-45. https://doi.org/10.36890/iejg.592276
AMA Perktaş SY, Keleş S. RICCI SOLITONS IN 3-DIMENSIONAL NORMAL ALMOST PARACONTACT METRIC MANIFOLDS. Int. Electron. J. Geom. October 2015;8(2):34-45. doi:10.36890/iejg.592276
Chicago Perktaş, Selcen Yüksel, and Sadik Keleş. “RICCI SOLITONS IN 3-DIMENSIONAL NORMAL ALMOST PARACONTACT METRIC MANIFOLDS”. International Electronic Journal of Geometry 8, no. 2 (October 2015): 34-45. https://doi.org/10.36890/iejg.592276.
EndNote Perktaş SY, Keleş S (October 1, 2015) RICCI SOLITONS IN 3-DIMENSIONAL NORMAL ALMOST PARACONTACT METRIC MANIFOLDS. International Electronic Journal of Geometry 8 2 34–45.
IEEE S. Y. Perktaş and S. Keleş, “RICCI SOLITONS IN 3-DIMENSIONAL NORMAL ALMOST PARACONTACT METRIC MANIFOLDS”, Int. Electron. J. Geom., vol. 8, no. 2, pp. 34–45, 2015, doi: 10.36890/iejg.592276.
ISNAD Perktaş, Selcen Yüksel - Keleş, Sadik. “RICCI SOLITONS IN 3-DIMENSIONAL NORMAL ALMOST PARACONTACT METRIC MANIFOLDS”. International Electronic Journal of Geometry 8/2 (October 2015), 34-45. https://doi.org/10.36890/iejg.592276.
JAMA Perktaş SY, Keleş S. RICCI SOLITONS IN 3-DIMENSIONAL NORMAL ALMOST PARACONTACT METRIC MANIFOLDS. Int. Electron. J. Geom. 2015;8:34–45.
MLA Perktaş, Selcen Yüksel and Sadik Keleş. “RICCI SOLITONS IN 3-DIMENSIONAL NORMAL ALMOST PARACONTACT METRIC MANIFOLDS”. International Electronic Journal of Geometry, vol. 8, no. 2, 2015, pp. 34-45, doi:10.36890/iejg.592276.
Vancouver Perktaş SY, Keleş S. RICCI SOLITONS IN 3-DIMENSIONAL NORMAL ALMOST PARACONTACT METRIC MANIFOLDS. Int. Electron. J. Geom. 2015;8(2):34-45.

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