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Pseudo Symmetric and Pseudo Ricci Symmetric $N(k)$-Contact Metric Manifolds

Yıl 2018, Cilt: 6 Sayı: 1, 134 - 139, 15.04.2018

S.v. Vishnuvardhana Venkatesha Venkatesha

Öz

The purpose of the present paper is to study the existence of pseudo symmetric, pseudo Ricci symmetric and generalized Ricci recurrent $N(k)$-contact metric manifolds.

Anahtar Kelimeler

Generalized Ricci recurrent manifolds; $N(k)$-contact metric manifolds Pseudo symmetric Pseudo Ricci symmetric manifolds

Kaynakça

  • [1] D.E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics, 509 Springer-Verlag, Berlin, 1976.
  • [2] D.E. Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Math., Birkhauser, Boston, 2002.
  • [3] D.E. Blair, Two remarks on contact metric structures, Tohoku Math. J., 29, 1977, 319-324.
  • [4] D.E. Blair, T. Koufogiorgos and B.J. Papantoniou, Contact metric manifolds satisfying a nullity condition, Israel J. Math., 91, 1995, 189-214.
  • [5] D.E. Blair, J.S. Kim and M.M. Tripathi, On the concircular curvature tensor of a contact metric manifold, J. Korean Math. Soc., 42(5), 2005, 883-992.
  • [6] E. Cartan, Surune classe remarquable despaces de Riema, Bulletin de la Soc. Math., France, 54, 1926, 214-264.
  • [7] M.C. Chaki, On conformally flat Pseudo-Ricci Symmetric Manifolds, Period. Math. Hungar., 19, 1988, 209-215.
  • [8] M.C. Chaki, On pseudosymmetric manifolds, An. Stiint. Univ., Al. I. Cuza Iasi, 33, 1987, 53-58.
  • [9] M.C. Chaki, On pseudo Ricci symmetric manifolds, Bulg. J. Phys. 15, 1988, 526-531.
  • [10] A. De, C-Bochner Curvature Tensor on N(k)-Contact Metric Manifolds, Lobachevskii Journal of Mathematics, 31(3), 2010, 209-214.
  • [11] U.C. De, N. Guha and D. Kamilya, On generalized Ricci-recurrent manifolds, Tensor (NS), 56, 1995, 312-317.
  • [12] U.C. De and S. Bandyopadhyay, On weakly symmetric Riemannian spaces, Publ. Math. Debrecen, 54, 1999, 377-381.
  • [13] U.C. De and P. Majhi, On a Type of Contact Metric Manifolds, Lobachevskii Journal of Mathematics, 34(1), 2013, 89-98.
  • [14] R. Deszcz, On pseudosymmetric spaces, Acta Math., Hungarica, 53, 1992, 185-190.
  • [15] J.A. Oubina, New classes of contact metric structures, Publ. Math. Debrecen., 32, 1985, 187-193.
  • [16] E.M. Patterson, Some theorems on Ricci-recurrent spaces, J Lond Math Soc., 27, 1952, 287-295.
  • [17] Rajendra Prasad, Vibha Srivastava and Shyam Kishor, On generalized Ricci-recurrent N(k)-contact metric manifods, Journal of National Academy of Mathematics, India.
  • [18] S. Sasaki, Lecture Note on almost Contact Manifolds, Part I, Tohoku Univ., Tohoku 1965.
  • [19] S. Sasaki, Lecture Note on almost Contact Manifolds, Part II, Tohoku Univ., Tohoku 1967.
  • [20] A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to dirichlet series, Indian Math. Soc., 20, 1956, 47-87.
  • [21] Z.I. Szabo, Structure theorems on Riemannian spaces satisfying R(X, Y) . R = 0. I, The local version, J. Differential Geom., 17(4), 1982, 531-582.
  • [22] L. Tamassy and T.Q. Binh, On weakly symmetric and weakly projective symmetric Rimannian manifolds, Coll. Math. Soc., J. Bolyai, 50, 1989, 663-670.
  • [23] L. Tamassy and T.Q. Binh, On weak symmetries of Einstein and Sasakian manifolds, Tensor, N. S., 53, 1993, 140-148.
  • [24] S. Tanno, The automorphism groups of almost contact Riemannian manifolds, Tohoku Math. J., 21, 1969, 21-38.
  • [25] S. Tanno, Ricci curvature of contact Riemannian manifolds, Tohoku Math. J., 40, 1988, 441-448.
  • [26] M. Tarafdar, On Pseudo Symmetric and Pseudo Ricci Symmetric Sasakian manifolds, Per. Math. Hung. 22(2), 1991, 125-129.
  • [27] M. Tarafdar and U.C. De, On pseudo symmetric and pseudo ricci symmetric K-contact manifolds, Per. Math. Hung. 31(1), 1995, 21-25.
  • [28] M. Tarafdar, On Pseudo Symmetric and Pseudo Ricci Symmetric P-Sasakian manifolds, Analele Stiintifice ale Universitatii Al. I. Cuza din Iasi. Serie Noua. Matematica, 37(2), 1991.
  • [29] Venkatesha and R.T. Naveen Kumar, Qausi conformal curvature tensor on N(k)-contact metric manifolds, Acta Math. Univ. Comenianae, LXXXV(1), 2016, 125-134.
  • [30] K. Yano, Concircular geometry I. Concircular transformations, Proc. Imp. Acad. Tokyo, 16, 1940, 195-200.
  • [31] A.A. Walker, On Ruses spaces of recurrent curvature, Proc. London Math. Soc., 52, 1950, 36-64.

Yıl 2018, Cilt: 6 Sayı: 1, 134 - 139, 15.04.2018

S.v. Vishnuvardhana Venkatesha Venkatesha

Öz

Kaynakça

  • [1] D.E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics, 509 Springer-Verlag, Berlin, 1976.
  • [2] D.E. Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Math., Birkhauser, Boston, 2002.
  • [3] D.E. Blair, Two remarks on contact metric structures, Tohoku Math. J., 29, 1977, 319-324.
  • [4] D.E. Blair, T. Koufogiorgos and B.J. Papantoniou, Contact metric manifolds satisfying a nullity condition, Israel J. Math., 91, 1995, 189-214.
  • [5] D.E. Blair, J.S. Kim and M.M. Tripathi, On the concircular curvature tensor of a contact metric manifold, J. Korean Math. Soc., 42(5), 2005, 883-992.
  • [6] E. Cartan, Surune classe remarquable despaces de Riema, Bulletin de la Soc. Math., France, 54, 1926, 214-264.
  • [7] M.C. Chaki, On conformally flat Pseudo-Ricci Symmetric Manifolds, Period. Math. Hungar., 19, 1988, 209-215.
  • [8] M.C. Chaki, On pseudosymmetric manifolds, An. Stiint. Univ., Al. I. Cuza Iasi, 33, 1987, 53-58.
  • [9] M.C. Chaki, On pseudo Ricci symmetric manifolds, Bulg. J. Phys. 15, 1988, 526-531.
  • [10] A. De, C-Bochner Curvature Tensor on N(k)-Contact Metric Manifolds, Lobachevskii Journal of Mathematics, 31(3), 2010, 209-214.
  • [11] U.C. De, N. Guha and D. Kamilya, On generalized Ricci-recurrent manifolds, Tensor (NS), 56, 1995, 312-317.
  • [12] U.C. De and S. Bandyopadhyay, On weakly symmetric Riemannian spaces, Publ. Math. Debrecen, 54, 1999, 377-381.
  • [13] U.C. De and P. Majhi, On a Type of Contact Metric Manifolds, Lobachevskii Journal of Mathematics, 34(1), 2013, 89-98.
  • [14] R. Deszcz, On pseudosymmetric spaces, Acta Math., Hungarica, 53, 1992, 185-190.
  • [15] J.A. Oubina, New classes of contact metric structures, Publ. Math. Debrecen., 32, 1985, 187-193.
  • [16] E.M. Patterson, Some theorems on Ricci-recurrent spaces, J Lond Math Soc., 27, 1952, 287-295.
  • [17] Rajendra Prasad, Vibha Srivastava and Shyam Kishor, On generalized Ricci-recurrent N(k)-contact metric manifods, Journal of National Academy of Mathematics, India.
  • [18] S. Sasaki, Lecture Note on almost Contact Manifolds, Part I, Tohoku Univ., Tohoku 1965.
  • [19] S. Sasaki, Lecture Note on almost Contact Manifolds, Part II, Tohoku Univ., Tohoku 1967.
  • [20] A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to dirichlet series, Indian Math. Soc., 20, 1956, 47-87.
  • [21] Z.I. Szabo, Structure theorems on Riemannian spaces satisfying R(X, Y) . R = 0. I, The local version, J. Differential Geom., 17(4), 1982, 531-582.
  • [22] L. Tamassy and T.Q. Binh, On weakly symmetric and weakly projective symmetric Rimannian manifolds, Coll. Math. Soc., J. Bolyai, 50, 1989, 663-670.
  • [23] L. Tamassy and T.Q. Binh, On weak symmetries of Einstein and Sasakian manifolds, Tensor, N. S., 53, 1993, 140-148.
  • [24] S. Tanno, The automorphism groups of almost contact Riemannian manifolds, Tohoku Math. J., 21, 1969, 21-38.
  • [25] S. Tanno, Ricci curvature of contact Riemannian manifolds, Tohoku Math. J., 40, 1988, 441-448.
  • [26] M. Tarafdar, On Pseudo Symmetric and Pseudo Ricci Symmetric Sasakian manifolds, Per. Math. Hung. 22(2), 1991, 125-129.
  • [27] M. Tarafdar and U.C. De, On pseudo symmetric and pseudo ricci symmetric K-contact manifolds, Per. Math. Hung. 31(1), 1995, 21-25.
  • [28] M. Tarafdar, On Pseudo Symmetric and Pseudo Ricci Symmetric P-Sasakian manifolds, Analele Stiintifice ale Universitatii Al. I. Cuza din Iasi. Serie Noua. Matematica, 37(2), 1991.
  • [29] Venkatesha and R.T. Naveen Kumar, Qausi conformal curvature tensor on N(k)-contact metric manifolds, Acta Math. Univ. Comenianae, LXXXV(1), 2016, 125-134.
  • [30] K. Yano, Concircular geometry I. Concircular transformations, Proc. Imp. Acad. Tokyo, 16, 1940, 195-200.
  • [31] A.A. Walker, On Ruses spaces of recurrent curvature, Proc. London Math. Soc., 52, 1950, 36-64.
Toplam 31 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

S.v. Vishnuvardhana Bu kişi benim

Venkatesha Venkatesha

Yayımlanma Tarihi 15 Nisan 2018
Gönderilme Tarihi 14 Kasım 2017
Yayımlandığı Sayı Yıl 2018 Cilt: 6 Sayı: 1

Kaynak Göster

APA Vishnuvardhana, S., & Venkatesha, V. (2018). Pseudo Symmetric and Pseudo Ricci Symmetric $N(k)$-Contact Metric Manifolds. Konuralp Journal of Mathematics, 6(1), 134-139.
AMA Vishnuvardhana S, Venkatesha V. Pseudo Symmetric and Pseudo Ricci Symmetric $N(k)$-Contact Metric Manifolds. Konuralp J. Math. Nisan 2018;6(1):134-139.
Chicago Vishnuvardhana, S.v., ve Venkatesha Venkatesha. “Pseudo Symmetric and Pseudo Ricci Symmetric $N(k)$-Contact Metric Manifolds”. Konuralp Journal of Mathematics 6, sy. 1 (Nisan 2018): 134-39.
EndNote Vishnuvardhana S, Venkatesha V (01 Nisan 2018) Pseudo Symmetric and Pseudo Ricci Symmetric $N(k)$-Contact Metric Manifolds. Konuralp Journal of Mathematics 6 1 134–139.
IEEE S. Vishnuvardhana ve V. Venkatesha, “Pseudo Symmetric and Pseudo Ricci Symmetric $N(k)$-Contact Metric Manifolds”, Konuralp J. Math., c. 6, sy. 1, ss. 134–139, 2018.
ISNAD Vishnuvardhana, S.v. - Venkatesha, Venkatesha. “Pseudo Symmetric and Pseudo Ricci Symmetric $N(k)$-Contact Metric Manifolds”. Konuralp Journal of Mathematics 6/1 (Nisan 2018), 134-139.
JAMA Vishnuvardhana S, Venkatesha V. Pseudo Symmetric and Pseudo Ricci Symmetric $N(k)$-Contact Metric Manifolds. Konuralp J. Math. 2018;6:134–139.
MLA Vishnuvardhana, S.v. ve Venkatesha Venkatesha. “Pseudo Symmetric and Pseudo Ricci Symmetric $N(k)$-Contact Metric Manifolds”. Konuralp Journal of Mathematics, c. 6, sy. 1, 2018, ss. 134-9.
Vancouver Vishnuvardhana S, Venkatesha V. Pseudo Symmetric and Pseudo Ricci Symmetric $N(k)$-Contact Metric Manifolds. Konuralp J. Math. 2018;6(1):134-9.
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