ON PSEUDO-SYMMETRY CURVATURE CONDITIONS OF GENERALIZED $(k,\mu)$-PARACONTACT METRIC MANIFOLDS

Sourav Makhal; U. C. De

Araştırma Makalesi

ON PSEUDO-SYMMETRY CURVATURE CONDITIONS OF GENERALIZED $(k,\mu)$-PARACONTACT METRIC MANIFOLDS

Yıl 2017, Cilt: 5 Sayı: 2, 239 - 247, 15.10.2017

Sourav Makhal U. C. De

Öz

In this paper we investigate Ricci pseudo-symmetric and Ricci generalized pseudo-symmetric generalized $(k,\mu )$-paracontact metric manifolds. Besides this we characterize generalized $(k,\mu )$-paracontact metric manifolds satisfying the curvature conditions $Q(S,R)=0$ and $Q(S,g)=0$, where $S$, $R$ are the Ricci tensor and curvature tensor respectively. Several corollaries are also obtained.

Anahtar Kelimeler

Generalized $(k, \mu)$-paracontact metric manifold, Ricci pseudo-symmetric manifold, Ricci generalized pseudo-symmetric manifold, Einstein manifold

Kaynakça

[1] Blair, D.E., Koufogiorgos, T. and Papatoniou, B.J., Contact metric manifolds satisfying a nullity condition, Israel J. Math., 91(1995), 189-214.
[2] Calvaruso. G., Homogeneous paracontact metric three-manifolds, Illinois J. Math., 55(2011), 697-718.
[3] Calvaruso, G. and A. Zaeim, A complete classication of Ricci and Yamabe solitons of non-reductive homogeneous 4-spaces, J. Geom. Phys, 80(2014), 15-25.
[4] Calvaruso, G. and Martin-Molina. V., Paracontact metric structure on the unit tangent sphere bundle, Ann. Math. Pura Appl.194(2015), 1359-1380.
[5] Calvaruso, G. and Perrone, A., Ricci solitons in three-dimensional paracontact geometry, J. Geom. Phys, 98(2015), 1-12.
[6] Capplelletti-Montano, B., Kupeli Erken, I and Murathan, C., Nullity conditions in paracon- tact geometry, Diff. Geom. Appl. 30(2012), 665-693.
[7] Cappelletti-Montano, B., Carriazo, A., Martin-Molina, V., Sasaki-Einstein and paraSasaki- Einstein metics from $(k,\mu )$-structure, J. Geom. Phys, 73(2013), 20-36.
[8] Cappelletti-Montano, B. and Di Terlizzi, L., Geometric structure associated to a contact metric $(k,\mu )$-space, Pacic J. Math., 246(2010), 257-292.
[9] De, U.C., Han, Y. and Mandal, K., On para-sasakian manifolds satisfying certain Curvature Conditions, Filomat 31(2017), 1941-1947.
[10] De, U.C., Deshmukh, S. and Mandal, K., On three-dimensional N(k)-paracontact metric manifolds and Ricci solitons, to appear in Bull. Iranian Math. Soc.
[11] De, U.C. and Pathak, G., On 3-dimensional Kenmotsu manifolds, Indian J. Pure Appl. Math.,35(2004), 159-165.
[12] Jun, J.-B. and Kim, U.-K., On 3-dimensional almost contact metric manifolds, Kyungpook Math. J., 34(1994), 293-301.
[13] Kowalczyk, D., On some subclass of semi-symmetric manifolds, Soochow J. Math.,27(2001), 445-461.
[14] Kupeli Erken, I., Generalized $(\tilde k\neq-1,\tilde\mu)$-paracontact metric manifolds with $\xi(\tilde\mu)=0,$; Int. Electron. J. Geom., 8(2015), 77-93.
[15] Kupeli Erken, I. and Murathan, C., A complete study of three-dimensional paracontact $(k,\mu,\nu)$-spaces, arXiv: 1305.1511.
[16] Kaneyuki, S. and Williams, F.L, Almost paracontact and parahodge structure on manifolds, Nagoya Math. J. 99(1985), 173-187.
[17] L. Verstraelen, Comments on pseudo-symmetry in sense of R. Deszcz, in: Geometry and Topology of submanifolds, World Sci. Publication. 6(1994), 199-209.
[18] Szabo, Z. I., Structure theorems on Riemannian spaces satisfying $R(X,Y)\cdot R=0$ the local version, J. Diff. Geom. 17(1982), 531-582.
[19] Zamkovoy, S., Canonical connection on paracontact manifolds, Ann. Global Anal. Geom. 36(2009), 37-60.

Yıl 2017, Cilt: 5 Sayı: 2, 239 - 247, 15.10.2017

Sourav Makhal U. C. De

Öz

Kaynakça

[1] Blair, D.E., Koufogiorgos, T. and Papatoniou, B.J., Contact metric manifolds satisfying a nullity condition, Israel J. Math., 91(1995), 189-214.
[2] Calvaruso. G., Homogeneous paracontact metric three-manifolds, Illinois J. Math., 55(2011), 697-718.
[3] Calvaruso, G. and A. Zaeim, A complete classication of Ricci and Yamabe solitons of non-reductive homogeneous 4-spaces, J. Geom. Phys, 80(2014), 15-25.
[4] Calvaruso, G. and Martin-Molina. V., Paracontact metric structure on the unit tangent sphere bundle, Ann. Math. Pura Appl.194(2015), 1359-1380.
[5] Calvaruso, G. and Perrone, A., Ricci solitons in three-dimensional paracontact geometry, J. Geom. Phys, 98(2015), 1-12.
[6] Capplelletti-Montano, B., Kupeli Erken, I and Murathan, C., Nullity conditions in paracon- tact geometry, Diff. Geom. Appl. 30(2012), 665-693.
[7] Cappelletti-Montano, B., Carriazo, A., Martin-Molina, V., Sasaki-Einstein and paraSasaki- Einstein metics from $(k,\mu )$-structure, J. Geom. Phys, 73(2013), 20-36.
[8] Cappelletti-Montano, B. and Di Terlizzi, L., Geometric structure associated to a contact metric $(k,\mu )$-space, Pacic J. Math., 246(2010), 257-292.
[9] De, U.C., Han, Y. and Mandal, K., On para-sasakian manifolds satisfying certain Curvature Conditions, Filomat 31(2017), 1941-1947.
[10] De, U.C., Deshmukh, S. and Mandal, K., On three-dimensional N(k)-paracontact metric manifolds and Ricci solitons, to appear in Bull. Iranian Math. Soc.
[11] De, U.C. and Pathak, G., On 3-dimensional Kenmotsu manifolds, Indian J. Pure Appl. Math.,35(2004), 159-165.
[12] Jun, J.-B. and Kim, U.-K., On 3-dimensional almost contact metric manifolds, Kyungpook Math. J., 34(1994), 293-301.
[13] Kowalczyk, D., On some subclass of semi-symmetric manifolds, Soochow J. Math.,27(2001), 445-461.
[14] Kupeli Erken, I., Generalized $(\tilde k\neq-1,\tilde\mu)$-paracontact metric manifolds with $\xi(\tilde\mu)=0,$; Int. Electron. J. Geom., 8(2015), 77-93.
[15] Kupeli Erken, I. and Murathan, C., A complete study of three-dimensional paracontact $(k,\mu,\nu)$-spaces, arXiv: 1305.1511.
[16] Kaneyuki, S. and Williams, F.L, Almost paracontact and parahodge structure on manifolds, Nagoya Math. J. 99(1985), 173-187.
[17] L. Verstraelen, Comments on pseudo-symmetry in sense of R. Deszcz, in: Geometry and Topology of submanifolds, World Sci. Publication. 6(1994), 199-209.
[18] Szabo, Z. I., Structure theorems on Riemannian spaces satisfying $R(X,Y)\cdot R=0$ the local version, J. Diff. Geom. 17(1982), 531-582.
[19] Zamkovoy, S., Canonical connection on paracontact manifolds, Ann. Global Anal. Geom. 36(2009), 37-60.

Toplam 19 adet kaynakça vardır.

Ayrıntılar

Konular	Mühendislik
Bölüm	Articles
Yazarlar	Sourav Makhal Bu kişi benim U. C. De
Yayımlanma Tarihi	15 Ekim 2017
Gönderilme Tarihi	19 Temmuz 2017
Kabul Tarihi	4 Ekim 2017
Yayımlandığı Sayı	Yıl 2017 Cilt: 5 Sayı: 2

Kaynak Göster

APA	Makhal, S., & De, U. C. (2017). ON PSEUDO-SYMMETRY CURVATURE CONDITIONS OF GENERALIZED $(k,\mu)$-PARACONTACT METRIC MANIFOLDS. Konuralp Journal of Mathematics, 5(2), 239-247.
AMA	Makhal S, De UC. ON PSEUDO-SYMMETRY CURVATURE CONDITIONS OF GENERALIZED $(k,\mu)$-PARACONTACT METRIC MANIFOLDS. Konuralp J. Math. Ekim 2017;5(2):239-247.
Chicago	Makhal, Sourav, ve U. C. De. “ON PSEUDO-SYMMETRY CURVATURE CONDITIONS OF GENERALIZED $(k,\mu)$-PARACONTACT METRIC MANIFOLDS”. Konuralp Journal of Mathematics 5, sy. 2 (Ekim 2017): 239-47.
EndNote	Makhal S, De UC (01 Ekim 2017) ON PSEUDO-SYMMETRY CURVATURE CONDITIONS OF GENERALIZED $(k,\mu)$-PARACONTACT METRIC MANIFOLDS. Konuralp Journal of Mathematics 5 2 239–247.
IEEE	S. Makhal ve U. C. De, “ON PSEUDO-SYMMETRY CURVATURE CONDITIONS OF GENERALIZED $(k,\mu)$-PARACONTACT METRIC MANIFOLDS”, Konuralp J. Math., c. 5, sy. 2, ss. 239–247, 2017.
ISNAD	Makhal, Sourav - De, U. C. “ON PSEUDO-SYMMETRY CURVATURE CONDITIONS OF GENERALIZED $(k,\mu)$-PARACONTACT METRIC MANIFOLDS”. Konuralp Journal of Mathematics 5/2 (Ekim 2017), 239-247.
JAMA	Makhal S, De UC. ON PSEUDO-SYMMETRY CURVATURE CONDITIONS OF GENERALIZED $(k,\mu)$-PARACONTACT METRIC MANIFOLDS. Konuralp J. Math. 2017;5:239–247.
MLA	Makhal, Sourav ve U. C. De. “ON PSEUDO-SYMMETRY CURVATURE CONDITIONS OF GENERALIZED $(k,\mu)$-PARACONTACT METRIC MANIFOLDS”. Konuralp Journal of Mathematics, c. 5, sy. 2, 2017, ss. 239-47.
Vancouver	Makhal S, De UC. ON PSEUDO-SYMMETRY CURVATURE CONDITIONS OF GENERALIZED $(k,\mu)$-PARACONTACT METRIC MANIFOLDS. Konuralp J. Math. 2017;5(2):239-47.

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