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

Year 2018, Volume: 6 Issue: 1, 134 - 139, 15.04.2018

S.v. Vishnuvardhana Venkatesha Venkatesha

Abstract

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.

Keywords

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

References

  • [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.

Year 2018, Volume: 6 Issue: 1, 134 - 139, 15.04.2018

S.v. Vishnuvardhana Venkatesha Venkatesha

Abstract

References

  • [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.
There are 31 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

S.v. Vishnuvardhana This is me

Venkatesha Venkatesha

Publication Date April 15, 2018
Submission Date November 14, 2017
Published in Issue Year 2018 Volume: 6 Issue: 1

Cite

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. April 2018;6(1):134-139.
Chicago Vishnuvardhana, S.v., and Venkatesha Venkatesha. “Pseudo Symmetric and Pseudo Ricci Symmetric $N(k)$-Contact Metric Manifolds”. Konuralp Journal of Mathematics 6, no. 1 (April 2018): 134-39.
EndNote Vishnuvardhana S, Venkatesha V (April 1, 2018) Pseudo Symmetric and Pseudo Ricci Symmetric $N(k)$-Contact Metric Manifolds. Konuralp Journal of Mathematics 6 1 134–139.
IEEE S. Vishnuvardhana and V. Venkatesha, “Pseudo Symmetric and Pseudo Ricci Symmetric $N(k)$-Contact Metric Manifolds”, Konuralp J. Math., vol. 6, no. 1, pp. 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 (April 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. and Venkatesha Venkatesha. “Pseudo Symmetric and Pseudo Ricci Symmetric $N(k)$-Contact Metric Manifolds”. Konuralp Journal of Mathematics, vol. 6, no. 1, 2018, pp. 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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