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Generalized projective curvature tensor of nearly cosymplectic manifold

Year 2020, Volume: 69 Issue: 1, 183 - 192, 30.06.2020
https://doi.org/10.31801/cfsuasmas.421435

Abstract

In this paper, we concentrated our attention on geometry of generalized projective tensor of nearly cosymplectic manifold. In particular, we studied the flatness property of generalized projective tensor. This property helped us to find the necessary and sufficient condition that nearly cosymplectic manifold is a generalized Einstein manifold.

References

  • Abood, H. M., Abd Ali, H. G., Geometry of Projective Tensor of Viasman-Gray Manifold, British Journal of Mathematics and Computer Science, V. 14, No. 6, (2016), 1-9.
  • Abood, H. M., Abd Ali, H. G., Projective-Recurrent Viasman-Gray manifold, Asian Journal of Mathematics and Computer Research, V. 13, No. 3, (2016), 184-191.
  • Abood, H. M., Holomorphic-geodesic transformation of almost Hermitian manifold, Ph.D. thesis, Moscow state University, Moscow, 2002.
  • Abood, H. M., Mohammed N. J., Locally Conformal Kähler Manifold of Pointwise Holomorphic Sectional Curvature Tensor, International Mathematical Forum, V. 5, No. 45, (2010), 2213-2224.
  • Abood, H. M., Mohammed N. J., Nearly Cosymplectic Manifold of Holomorphic Sectional Curvature Tensor, Far East Journal of Mathematical Science, V. 106, No. 1, (2018), 171-181.
  • Atceken, M., On Generalized Sasakian Space Forms Satisfying Certain Conditions On The Concircular Curvature Tensor, Bulletain of Mathematical Analysis and Applications, V. 6, (2014), 1-8.
  • Atceken, M., Yildirim U., Almost C(α)-manifolds Satisfying Certain Conditions, Advanced Studies in Contemporary Mathematics, V. 26, N. 3, (2016), 567-578.
  • Blair, D. E., The Theory of Quasi - Sasakian Structures, J. Differential Geometry, No. 1, (1967), 331-345.
  • Blair, D.E., Showders D.K., Yano K., Nearly Sasakian Structure, Kodoi Math. Sem. Rep. 27, No. 1-2, (1976), 175-180.
  • Gan, G., Characteristic of Some Classes of Almost Hermitian Manifolds, Serdica, V. 4, (1978), 19-23.
  • Kirichenko, V. F., Differential geometry of K-space, Problems of Geometry, V.8, (1977), 139-160.
  • Kirichenko, V. F., Sur le geometrie des varietes approximativent cosymlectiques, C. R. Acad. Sci. Paris, 295, (1983), 673-676.
  • Kirichenko, V. F., The Method of Generalization of Hermitian Geometry in The Almost Hermitian Contact Manifold, Problems of geometry VINITE ANSSR , V. 18, (1986), 25-71.
  • Kirichenko, V. F., Differential - Geometry Structures on Manifolds, Second edition, expanded. Odessa, Printing House, p. 458, 2013.
  • Kirichenko, V. F. and Kusova, E. V., On Geometry of Weakly Co-symplectic Manifold, Journal of Mathematical Sciences, 177, (2011), 668.
  • Kirichenko, V. F. and Rustanov, A. R. Differential Geometry of Quasi-Sasakian Manifolds, Mathematical Collection, V. 193, No. 8, (2002), 71-100.
  • Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry, John Wily and Sons, V.1, 1963.
  • Mileva, P., Locally Conformally Kähler Manifolds of Constant Type and J-Invariant Curvature Tensor, Facta universitatis, Series: Mechanics, Automatic control and Robotics, V. 3, No. 14, (2003), 791-804.
  • Petrov, A. Z., Einstein Space, Phys-Math. Letr., Moscow, (1961), p. 463.
  • Shashikala, S., Venkatesha, On Generalized Psedo-Projective [varPhi]<LaTeX>\varPhi</LaTeX>-Recurrent (k)-Contact Metric Manifold, International J. of scientific and research puplications, V.4, Issue 3, (2014), 2250-3153.
  • Yildirim, U., Atceken, M., On The C(α)-manifolds Satisfying Certain Conditions On Quasi-Conformal Curvature Tensor, Proceding of the Jangjeon Mathematical Society, V.19, N. 1, (2016), p.115-124.
  • Yildirim, U., Atceken, M. and Dirik, S., Pseudo Projective Curvature Tensor Satisfying Some Properties On A Normal Paracontact Metric Manifold, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., V. 68, No.1, (2019), 997-1016.
Year 2020, Volume: 69 Issue: 1, 183 - 192, 30.06.2020
https://doi.org/10.31801/cfsuasmas.421435

Abstract

References

  • Abood, H. M., Abd Ali, H. G., Geometry of Projective Tensor of Viasman-Gray Manifold, British Journal of Mathematics and Computer Science, V. 14, No. 6, (2016), 1-9.
  • Abood, H. M., Abd Ali, H. G., Projective-Recurrent Viasman-Gray manifold, Asian Journal of Mathematics and Computer Research, V. 13, No. 3, (2016), 184-191.
  • Abood, H. M., Holomorphic-geodesic transformation of almost Hermitian manifold, Ph.D. thesis, Moscow state University, Moscow, 2002.
  • Abood, H. M., Mohammed N. J., Locally Conformal Kähler Manifold of Pointwise Holomorphic Sectional Curvature Tensor, International Mathematical Forum, V. 5, No. 45, (2010), 2213-2224.
  • Abood, H. M., Mohammed N. J., Nearly Cosymplectic Manifold of Holomorphic Sectional Curvature Tensor, Far East Journal of Mathematical Science, V. 106, No. 1, (2018), 171-181.
  • Atceken, M., On Generalized Sasakian Space Forms Satisfying Certain Conditions On The Concircular Curvature Tensor, Bulletain of Mathematical Analysis and Applications, V. 6, (2014), 1-8.
  • Atceken, M., Yildirim U., Almost C(α)-manifolds Satisfying Certain Conditions, Advanced Studies in Contemporary Mathematics, V. 26, N. 3, (2016), 567-578.
  • Blair, D. E., The Theory of Quasi - Sasakian Structures, J. Differential Geometry, No. 1, (1967), 331-345.
  • Blair, D.E., Showders D.K., Yano K., Nearly Sasakian Structure, Kodoi Math. Sem. Rep. 27, No. 1-2, (1976), 175-180.
  • Gan, G., Characteristic of Some Classes of Almost Hermitian Manifolds, Serdica, V. 4, (1978), 19-23.
  • Kirichenko, V. F., Differential geometry of K-space, Problems of Geometry, V.8, (1977), 139-160.
  • Kirichenko, V. F., Sur le geometrie des varietes approximativent cosymlectiques, C. R. Acad. Sci. Paris, 295, (1983), 673-676.
  • Kirichenko, V. F., The Method of Generalization of Hermitian Geometry in The Almost Hermitian Contact Manifold, Problems of geometry VINITE ANSSR , V. 18, (1986), 25-71.
  • Kirichenko, V. F., Differential - Geometry Structures on Manifolds, Second edition, expanded. Odessa, Printing House, p. 458, 2013.
  • Kirichenko, V. F. and Kusova, E. V., On Geometry of Weakly Co-symplectic Manifold, Journal of Mathematical Sciences, 177, (2011), 668.
  • Kirichenko, V. F. and Rustanov, A. R. Differential Geometry of Quasi-Sasakian Manifolds, Mathematical Collection, V. 193, No. 8, (2002), 71-100.
  • Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry, John Wily and Sons, V.1, 1963.
  • Mileva, P., Locally Conformally Kähler Manifolds of Constant Type and J-Invariant Curvature Tensor, Facta universitatis, Series: Mechanics, Automatic control and Robotics, V. 3, No. 14, (2003), 791-804.
  • Petrov, A. Z., Einstein Space, Phys-Math. Letr., Moscow, (1961), p. 463.
  • Shashikala, S., Venkatesha, On Generalized Psedo-Projective [varPhi]<LaTeX>\varPhi</LaTeX>-Recurrent (k)-Contact Metric Manifold, International J. of scientific and research puplications, V.4, Issue 3, (2014), 2250-3153.
  • Yildirim, U., Atceken, M., On The C(α)-manifolds Satisfying Certain Conditions On Quasi-Conformal Curvature Tensor, Proceding of the Jangjeon Mathematical Society, V.19, N. 1, (2016), p.115-124.
  • Yildirim, U., Atceken, M. and Dirik, S., Pseudo Projective Curvature Tensor Satisfying Some Properties On A Normal Paracontact Metric Manifold, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., V. 68, No.1, (2019), 997-1016.
There are 22 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Habeeb Abood 0000-0002-3257-9550

Nawaf Mohammed This is me 0000-0002-5426-1447

Publication Date June 30, 2020
Submission Date June 20, 2018
Acceptance Date September 30, 2019
Published in Issue Year 2020 Volume: 69 Issue: 1

Cite

APA Abood, H., & Mohammed, N. (2020). Generalized projective curvature tensor of nearly cosymplectic manifold. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(1), 183-192. https://doi.org/10.31801/cfsuasmas.421435
AMA Abood H, Mohammed N. Generalized projective curvature tensor of nearly cosymplectic manifold. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2020;69(1):183-192. doi:10.31801/cfsuasmas.421435
Chicago Abood, Habeeb, and Nawaf Mohammed. “Generalized Projective Curvature Tensor of Nearly Cosymplectic Manifold”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 1 (June 2020): 183-92. https://doi.org/10.31801/cfsuasmas.421435.
EndNote Abood H, Mohammed N (June 1, 2020) Generalized projective curvature tensor of nearly cosymplectic manifold. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 1 183–192.
IEEE H. Abood and N. Mohammed, “Generalized projective curvature tensor of nearly cosymplectic manifold”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 1, pp. 183–192, 2020, doi: 10.31801/cfsuasmas.421435.
ISNAD Abood, Habeeb - Mohammed, Nawaf. “Generalized Projective Curvature Tensor of Nearly Cosymplectic Manifold”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/1 (June 2020), 183-192. https://doi.org/10.31801/cfsuasmas.421435.
JAMA Abood H, Mohammed N. Generalized projective curvature tensor of nearly cosymplectic manifold. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:183–192.
MLA Abood, Habeeb and Nawaf Mohammed. “Generalized Projective Curvature Tensor of Nearly Cosymplectic Manifold”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 1, 2020, pp. 183-92, doi:10.31801/cfsuasmas.421435.
Vancouver Abood H, Mohammed N. Generalized projective curvature tensor of nearly cosymplectic manifold. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(1):183-92.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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