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BibTex RIS Kaynak Göster

Yıl 2016, Cilt: 4 Sayı: 3, 162 - 173, 30.09.2016

Bilal Eftal Acet Selcen Yüksel Perktaş

Öz

Kaynakça

  • B. E. Acet, S. Yüksel Perktaş, E. Kılıç, On lightlike geometry of para-Sasakian manifolds, Scientific Work J., Article ID 696231, 2014.
  • D. E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics, Vol. 509. Springer-Verlag, Berlin-New York, 1976.
  • B. E. Acet, E. Kiliç, S. Yüksel Perktaş, Some Curvature Conditions on a Para-Sasakian Manifold with Canonical Paracontact Connection, Int. J. of Math. and Math. Sci., Article ID 395462, 2012.
  • S. Kaneyuki, M. Konzai, Paracomplex structure and affine symmetric spaces, Tokyo J. Math., 8 (1985), 301-318.
  • S. Kaneyuki, F. L. Willams, Almost paracontact and parahodge structure on manifolds, Nagoya Math. J., 99 (1985), 173-187.
  • S. Sasaki, On differentiable manifolds with certain structures which are closely related to almost contact structure I, Tôhoku Math. J., 12 (1960), 459-476.
  • I. Sato, On a structure similar to the almost contact structure I., Tensor N. S., 30 (1976), 219-224.
  • I. Sato, On a structure similar to the almost contact structure II., Tensor N. S., 31 (1977), 199-205.
  • T. Takahashi, Sasakian manifold with pseudo-Riemannian metric, Tôhoku Math. J., 21 (1969), 644-653.
  • N. Tanaka, On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connection, Japan J. Math., 2 (1976), 131-190.
  • S. Tanno, Variational problems on contact Riemannian manifolds, Trans. Amer. Math. Soc., 314 (1989), 349-379.
  • S. M. Webster, Pseudo-Hermitian structures on a real hypersurfaces, J. Diff. Geo., 13 (1979), 25-41.
  • J. L. Cabrerizo, L. M. Fernandez, M. Fernandez, G. Zhen, The structuren of a class of K-contact manifolds, Acta Math. Hungarica, 82 (1999), 331-340.
  • K. Yano, Concircular geometry I , Concircular transformations, Proc. Imp. Acad.Tokyo, 16 (1940), 195-200.
  • K. Yano, S. Bochner, Curvature and Betti numbers, Annals of Mathematics Studies 32, Princeton University Press, 1953.
  • K. Yano, Affine connexions in almost product spaces, Kodai Math. Sem. Rep., 11 (1959), 1-24.
  • K. Yano, M. Kon, Structures on Manifolds, Series in Pure Math., Vol 3,World Sci, 1984.
  • S. Zamkovoy, Canonical connection on paracontact manifolds, Ann. Glob. Anal. Geo., 36 (2009), 37-60.

On para-Sasakian manifolds with a canonical paracontact connection

Yıl 2016, Cilt: 4 Sayı: 3, 162 - 173, 30.09.2016

Bilal Eftal Acet Selcen Yüksel Perktaş

Öz




The object of the present paper is to study a
para-Sasakian manifold with a canonical paracontact connection. We prove that conformally flat, concircularly flat and projectively flat para-Sasakian manifolds with respect to canonical
paracontact connection are all Einstein manifolds. Also, it is shown that a quasi-concircularly flat
para-Sasakian manifold is of constant scalar curvature.




Anahtar Kelimeler

Para-Sasakian manifold

Kaynakça

  • B. E. Acet, S. Yüksel Perktaş, E. Kılıç, On lightlike geometry of para-Sasakian manifolds, Scientific Work J., Article ID 696231, 2014.
  • D. E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics, Vol. 509. Springer-Verlag, Berlin-New York, 1976.
  • B. E. Acet, E. Kiliç, S. Yüksel Perktaş, Some Curvature Conditions on a Para-Sasakian Manifold with Canonical Paracontact Connection, Int. J. of Math. and Math. Sci., Article ID 395462, 2012.
  • S. Kaneyuki, M. Konzai, Paracomplex structure and affine symmetric spaces, Tokyo J. Math., 8 (1985), 301-318.
  • S. Kaneyuki, F. L. Willams, Almost paracontact and parahodge structure on manifolds, Nagoya Math. J., 99 (1985), 173-187.
  • S. Sasaki, On differentiable manifolds with certain structures which are closely related to almost contact structure I, Tôhoku Math. J., 12 (1960), 459-476.
  • I. Sato, On a structure similar to the almost contact structure I., Tensor N. S., 30 (1976), 219-224.
  • I. Sato, On a structure similar to the almost contact structure II., Tensor N. S., 31 (1977), 199-205.
  • T. Takahashi, Sasakian manifold with pseudo-Riemannian metric, Tôhoku Math. J., 21 (1969), 644-653.
  • N. Tanaka, On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connection, Japan J. Math., 2 (1976), 131-190.
  • S. Tanno, Variational problems on contact Riemannian manifolds, Trans. Amer. Math. Soc., 314 (1989), 349-379.
  • S. M. Webster, Pseudo-Hermitian structures on a real hypersurfaces, J. Diff. Geo., 13 (1979), 25-41.
  • J. L. Cabrerizo, L. M. Fernandez, M. Fernandez, G. Zhen, The structuren of a class of K-contact manifolds, Acta Math. Hungarica, 82 (1999), 331-340.
  • K. Yano, Concircular geometry I , Concircular transformations, Proc. Imp. Acad.Tokyo, 16 (1940), 195-200.
  • K. Yano, S. Bochner, Curvature and Betti numbers, Annals of Mathematics Studies 32, Princeton University Press, 1953.
  • K. Yano, Affine connexions in almost product spaces, Kodai Math. Sem. Rep., 11 (1959), 1-24.
  • K. Yano, M. Kon, Structures on Manifolds, Series in Pure Math., Vol 3,World Sci, 1984.
  • S. Zamkovoy, Canonical connection on paracontact manifolds, Ann. Glob. Anal. Geo., 36 (2009), 37-60.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Bilal Eftal Acet

Selcen Yüksel Perktaş Bu kişi benim

Yayımlanma Tarihi 30 Eylül 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 4 Sayı: 3

Kaynak Göster

APA Acet, B. E., & Perktaş, S. Y. (2016). On para-Sasakian manifolds with a canonical paracontact connection. New Trends in Mathematical Sciences, 4(3), 162-173.
AMA Acet BE, Perktaş SY. On para-Sasakian manifolds with a canonical paracontact connection. New Trends in Mathematical Sciences. Eylül 2016;4(3):162-173.
Chicago Acet, Bilal Eftal, ve Selcen Yüksel Perktaş. “On Para-Sasakian Manifolds With a Canonical Paracontact Connection”. New Trends in Mathematical Sciences 4, sy. 3 (Eylül 2016): 162-73.
EndNote Acet BE, Perktaş SY (01 Eylül 2016) On para-Sasakian manifolds with a canonical paracontact connection. New Trends in Mathematical Sciences 4 3 162–173.
IEEE B. E. Acet ve S. Y. Perktaş, “On para-Sasakian manifolds with a canonical paracontact connection”, New Trends in Mathematical Sciences, c. 4, sy. 3, ss. 162–173, 2016.
ISNAD Acet, Bilal Eftal - Perktaş, Selcen Yüksel. “On Para-Sasakian Manifolds With a Canonical Paracontact Connection”. New Trends in Mathematical Sciences 4/3 (Eylül 2016), 162-173.
JAMA Acet BE, Perktaş SY. On para-Sasakian manifolds with a canonical paracontact connection. New Trends in Mathematical Sciences. 2016;4:162–173.
MLA Acet, Bilal Eftal ve Selcen Yüksel Perktaş. “On Para-Sasakian Manifolds With a Canonical Paracontact Connection”. New Trends in Mathematical Sciences, c. 4, sy. 3, 2016, ss. 162-73.
Vancouver Acet BE, Perktaş SY. On para-Sasakian manifolds with a canonical paracontact connection. New Trends in Mathematical Sciences. 2016;4(3):162-73.
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