Three Dimensional Quasi-Para-Sasakian Manifolds Satisfying Certain Curvature Conditions

İrem Küpeli Erken

Araştırma Makalesi

Three Dimensional Quasi-Para-Sasakian Manifolds Satisfying Certain Curvature Conditions

Yıl 2018, Cilt: 6 Sayı: 2, 57 - 65, 31.10.2018

İrem Küpeli Erken

Öz

The object of the present paper is to study some classes of 3-dimensional quasi-para-Sasakian manifolds

with beta=const. We investigated 3-dimensional quasi-para-Sasakian manifolds with beta=const. satisfying

the curvature conditions P:Q = 0; Q:P = 0; P:R = 0, where P is the projective curvature tensor, Q is

the Ricci operator and R is the Riemannian curvature tensor. Also, a 3-dimensional concircularly flat

quasi-para-Sasakian manifold with beta=const. is studied. Finally, an example of 3-dimensional proper

quasi-para-Sasakian manifold with beta =const. is given.

Anahtar Kelimeler

quasi-para-Sasakian manifold, Einstein manifold, concircularly flat, Projective curvature tensor

Kaynakça

[1] Bejan, C. L. and Crasmareanu M., Second order parallel tensors and Ricci solitons in 3-dimensional normal paracontact geometry, Ann. Global Anal. Geom. 46(2) (2014), 117–127.
[2] Besse, A. L., Einstein manifolds, Springer-verlag, Berlin-Heidelberg (1987).
[3] Blair, D. E., The theory of quasi-Sasakian structures, J. Differential Geom. 1 (1967), 331–345.
[4] Blair, D. E., Riemannian Geometry of Contact and Symplectic Manifolds, Progress in Mathematics Vol. 203, Birkhäuser, Boston, 2002.
[5] Cappelletti-Montano, B., Küpeli Erken, I. and Murathan, C., Nullity conditions in paracontact geometry, Diff. Geom. Appl. 30 (2012), 665–693.
[6] Dacko, P., On almost para-cosymplectic manifolds, Tsukuba J. Math. 28 (2004), 193–213.
[7] Deszcz, R., Verstraelen L. and Yaprak S.,Warped products realizing a certain conditions of pseudosymmetry type imposed on theWeyl curvature tensor, Chin. J. Math. 22(1994), 139-157.
[8] Erdem, S., On almost (para)contact (hyperbolic) metric manifolds and harmonicity of ('; '0)- holomorphic maps between them, Houston J. Math. 28 (2002), 21–45.
[9] Kanemaki, S., Quasi-Sasakian manifolds, Tohoku Math. J. 29 (1977), 227–233.
[10] Kaneyuki, S. and Williams, F. L., Almost paracontact and parahodge structures on manifolds, Nagoya Math. J 1985; 99: 173–187.
[11] Küpeli Erken, I., Some classes of 3-dimensional normal almost paracontact metric manifolds, Honam Math. J. 37, no. 4 (2015), 457-468.
[12] Küpeli Erken, I., On normal almost paracontact metric manifolds of dimension 3, Facta Univ. Ser. Math. Inform. 30, no. 5 (2015), 777-788.
[13] Küpeli Erken, I., Dacko, P., Murathan, C. Almost 􀀀 paracosymplectic manifolds, J. Geom. Phys. 88, (2015), 30-51.
[14] Majhi, P. and Ghosh, G., On a classification of parasasakian manifolds, Facta Univ. Ser. Math. Inform. 32, No 5 (2017), 781-788.
[15] Olszak, Z., Curvature properties of quasi-Sasakian manifolds, Tensor 38 (1982), 19–28.
[16] Olszak, Z., Normal almost contact metric manifolds of dimension three, Ann. Polon. Math. XLVII (1986), 41–50.
[17] Soos, G., Über die geodätischen Abbildungen von Riemannaschen R äumen auf projektiv symmetrische Riemannsche Räume, Acta. Math. Acad. Sci. Hungar. Tom 9 (1958) 359-361.
[18] Tanno, S., Quasi-Sasakian structures of rank 2p + 1, J. Differential Geom. 5 (1971), 317–324.
[19] Wełyczko, J., On basic curvature identities for almost (para)contact metric manifolds. Available in Arxiv: 1209.4731 [math. DG].
[20] Welyczko, J., On Legendre Curves in 3-Dimensional Normal Almost Paracontact Metric Manifolds, Result. Math. 54 (2009), 377–387.
[21] Yano, K., Concircular geometry I, Concircular transformations, Proc. Imp. Acad. Tokyo, 16 (1940) 195-200.
[22] Yano, K. and Bochner, S., Curvature and Betti numbers, Annals of mathematics studies, 32, Princeton university press,1953.
[23] Zamkovoy, S., Canonical connections on paracontact manifolds, Ann. Glob. Anal. Geom. 36 (2009), 37–60.

Yıl 2018, Cilt: 6 Sayı: 2, 57 - 65, 31.10.2018

İrem Küpeli Erken

Öz

Kaynakça

[1] Bejan, C. L. and Crasmareanu M., Second order parallel tensors and Ricci solitons in 3-dimensional normal paracontact geometry, Ann. Global Anal. Geom. 46(2) (2014), 117–127.
[2] Besse, A. L., Einstein manifolds, Springer-verlag, Berlin-Heidelberg (1987).
[3] Blair, D. E., The theory of quasi-Sasakian structures, J. Differential Geom. 1 (1967), 331–345.
[4] Blair, D. E., Riemannian Geometry of Contact and Symplectic Manifolds, Progress in Mathematics Vol. 203, Birkhäuser, Boston, 2002.
[5] Cappelletti-Montano, B., Küpeli Erken, I. and Murathan, C., Nullity conditions in paracontact geometry, Diff. Geom. Appl. 30 (2012), 665–693.
[6] Dacko, P., On almost para-cosymplectic manifolds, Tsukuba J. Math. 28 (2004), 193–213.
[7] Deszcz, R., Verstraelen L. and Yaprak S.,Warped products realizing a certain conditions of pseudosymmetry type imposed on theWeyl curvature tensor, Chin. J. Math. 22(1994), 139-157.
[8] Erdem, S., On almost (para)contact (hyperbolic) metric manifolds and harmonicity of ('; '0)- holomorphic maps between them, Houston J. Math. 28 (2002), 21–45.
[9] Kanemaki, S., Quasi-Sasakian manifolds, Tohoku Math. J. 29 (1977), 227–233.
[10] Kaneyuki, S. and Williams, F. L., Almost paracontact and parahodge structures on manifolds, Nagoya Math. J 1985; 99: 173–187.
[11] Küpeli Erken, I., Some classes of 3-dimensional normal almost paracontact metric manifolds, Honam Math. J. 37, no. 4 (2015), 457-468.
[12] Küpeli Erken, I., On normal almost paracontact metric manifolds of dimension 3, Facta Univ. Ser. Math. Inform. 30, no. 5 (2015), 777-788.
[13] Küpeli Erken, I., Dacko, P., Murathan, C. Almost 􀀀 paracosymplectic manifolds, J. Geom. Phys. 88, (2015), 30-51.
[14] Majhi, P. and Ghosh, G., On a classification of parasasakian manifolds, Facta Univ. Ser. Math. Inform. 32, No 5 (2017), 781-788.
[15] Olszak, Z., Curvature properties of quasi-Sasakian manifolds, Tensor 38 (1982), 19–28.
[16] Olszak, Z., Normal almost contact metric manifolds of dimension three, Ann. Polon. Math. XLVII (1986), 41–50.
[17] Soos, G., Über die geodätischen Abbildungen von Riemannaschen R äumen auf projektiv symmetrische Riemannsche Räume, Acta. Math. Acad. Sci. Hungar. Tom 9 (1958) 359-361.
[18] Tanno, S., Quasi-Sasakian structures of rank 2p + 1, J. Differential Geom. 5 (1971), 317–324.
[19] Wełyczko, J., On basic curvature identities for almost (para)contact metric manifolds. Available in Arxiv: 1209.4731 [math. DG].
[20] Welyczko, J., On Legendre Curves in 3-Dimensional Normal Almost Paracontact Metric Manifolds, Result. Math. 54 (2009), 377–387.
[21] Yano, K., Concircular geometry I, Concircular transformations, Proc. Imp. Acad. Tokyo, 16 (1940) 195-200.
[22] Yano, K. and Bochner, S., Curvature and Betti numbers, Annals of mathematics studies, 32, Princeton university press,1953.
[23] Zamkovoy, S., Canonical connections on paracontact manifolds, Ann. Glob. Anal. Geom. 36 (2009), 37–60.

Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Bölüm	Articles
Yazarlar	İrem Küpeli Erken 0000-0003-4471-3291
Yayımlanma Tarihi	31 Ekim 2018
Gönderilme Tarihi	10 Temmuz 2018
Kabul Tarihi	21 Ekim 2018
Yayımlandığı Sayı	Yıl 2018 Cilt: 6 Sayı: 2

Kaynak Göster

APA	Küpeli Erken, İ. (2018). Three Dimensional Quasi-Para-Sasakian Manifolds Satisfying Certain Curvature Conditions. Mathematical Sciences and Applications E-Notes, 6(2), 57-65.
AMA	Küpeli Erken İ. Three Dimensional Quasi-Para-Sasakian Manifolds Satisfying Certain Curvature Conditions. Math. Sci. Appl. E-Notes. Ekim 2018;6(2):57-65.
Chicago	Küpeli Erken, İrem. “Three Dimensional Quasi-Para-Sasakian Manifolds Satisfying Certain Curvature Conditions”. Mathematical Sciences and Applications E-Notes 6, sy. 2 (Ekim 2018): 57-65.
EndNote	Küpeli Erken İ (01 Ekim 2018) Three Dimensional Quasi-Para-Sasakian Manifolds Satisfying Certain Curvature Conditions. Mathematical Sciences and Applications E-Notes 6 2 57–65.
IEEE	İ. Küpeli Erken, “Three Dimensional Quasi-Para-Sasakian Manifolds Satisfying Certain Curvature Conditions”, Math. Sci. Appl. E-Notes, c. 6, sy. 2, ss. 57–65, 2018.
ISNAD	Küpeli Erken, İrem. “Three Dimensional Quasi-Para-Sasakian Manifolds Satisfying Certain Curvature Conditions”. Mathematical Sciences and Applications E-Notes 6/2 (Ekim 2018), 57-65.
JAMA	Küpeli Erken İ. Three Dimensional Quasi-Para-Sasakian Manifolds Satisfying Certain Curvature Conditions. Math. Sci. Appl. E-Notes. 2018;6:57–65.
MLA	Küpeli Erken, İrem. “Three Dimensional Quasi-Para-Sasakian Manifolds Satisfying Certain Curvature Conditions”. Mathematical Sciences and Applications E-Notes, c. 6, sy. 2, 2018, ss. 57-65.
Vancouver	Küpeli Erken İ. Three Dimensional Quasi-Para-Sasakian Manifolds Satisfying Certain Curvature Conditions. Math. Sci. Appl. E-Notes. 2018;6(2):57-65.