[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.
[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
[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.
[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
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.