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COVARIENT DERIVATIVES OF ALMOST CONTACT STRUCTURE AND ALMOST PARACONTACT STRUCTURE WITH RESPECT TO $X^{C}$ AND $X^{V}$ ON TANGENT BUNDLE $T(M)$

Year 2016, Volume: 4 Issue: 2, 209 - 216, 01.10.2016

HASIM Cayır

Abstract

The differential geometry of tangent bundles was studied by several authors, for example: D. E. Blair \cite{B76}, V. Oproiu \cite{O73}, A. Salimov \cite% {S13}, Yano and Ishihara \cite{YI73} and among others. It is well known that differant structures deffined on a manifold $M$ can be lifted to the same type of structures on its tangent bundle. Several authors cited here in obtained result in this direction. Our goal is to study covarient derivatives of almost contact structure and almost paracontact structure with respect to $X^{C}$ and $X^{V}$ on tangent bundle $T(M)$. In addition, this covarient derivatives which obtained shall be studied for some special values in almost contact structure and almost paracontact structure.

Keywords

Covarient Derivative Almost Contact Structure Almost Paracontact Structure

References

  • [1] Blair, D. E., Contact Manifolds in Riemannian Geometry, Lecture Notes in Math, 509, Springer Verlag, New York, 1976.
  • [2] Das, Lovejoy S., Fiberings on almost r-contact manifolds, Publicationes Mathematicae, Debrecen, Hungary 43(1993), 161-167.
  • [3] Omran, T., Sharffuddin, A. and Husain, S. I., Lift of Structures on Manifolds, Publications de 1'Institut Mathematiqe, Nouvelle serie, 360(1984), no. 50, 93 { 97.
  • [4] Oproiu, V., Some remarkable structures and connexions, de ned on the tangent bundle, Rendiconti di Matematica 3(1973), 6 VI.
  • [5] Salimov, A. A., Tensor Operators and Their applications, Nova Science Publ., New York, 2013.
  • [6] Salimov, A. A. and Cayir, H., Some Notes On Almost Paracontact Structures, Comptes Rendus de 1'Acedemie Bulgare Des Sciences, 66(2013), no. 3, 331-338.
  • [7] Sasaki, S., On The Differantial Geometry of Tangent Boundles of Riemannian Manifolds, Tohoku Math. J., 10(1958), 338-358.
  • [8] Yano, K. and Ishihara, S., Tangent and Cotangent Bundles, Marcel Dekker Inc, New York, 1973

Year 2016, Volume: 4 Issue: 2, 209 - 216, 01.10.2016

HASIM Cayır

Abstract

References

  • [1] Blair, D. E., Contact Manifolds in Riemannian Geometry, Lecture Notes in Math, 509, Springer Verlag, New York, 1976.
  • [2] Das, Lovejoy S., Fiberings on almost r-contact manifolds, Publicationes Mathematicae, Debrecen, Hungary 43(1993), 161-167.
  • [3] Omran, T., Sharffuddin, A. and Husain, S. I., Lift of Structures on Manifolds, Publications de 1'Institut Mathematiqe, Nouvelle serie, 360(1984), no. 50, 93 { 97.
  • [4] Oproiu, V., Some remarkable structures and connexions, de ned on the tangent bundle, Rendiconti di Matematica 3(1973), 6 VI.
  • [5] Salimov, A. A., Tensor Operators and Their applications, Nova Science Publ., New York, 2013.
  • [6] Salimov, A. A. and Cayir, H., Some Notes On Almost Paracontact Structures, Comptes Rendus de 1'Acedemie Bulgare Des Sciences, 66(2013), no. 3, 331-338.
  • [7] Sasaki, S., On The Differantial Geometry of Tangent Boundles of Riemannian Manifolds, Tohoku Math. J., 10(1958), 338-358.
  • [8] Yano, K. and Ishihara, S., Tangent and Cotangent Bundles, Marcel Dekker Inc, New York, 1973
There are 8 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

HASIM Cayır

Publication Date October 1, 2016
Submission Date July 8, 2015
Published in Issue Year 2016 Volume: 4 Issue: 2

Cite

APA Cayır, H. (2016). COVARIENT DERIVATIVES OF ALMOST CONTACT STRUCTURE AND ALMOST PARACONTACT STRUCTURE WITH RESPECT TO $X^{C}$ AND $X^{V}$ ON TANGENT BUNDLE $T(M)$. Konuralp Journal of Mathematics, 4(2), 209-216.
AMA Cayır H. COVARIENT DERIVATIVES OF ALMOST CONTACT STRUCTURE AND ALMOST PARACONTACT STRUCTURE WITH RESPECT TO $X^{C}$ AND $X^{V}$ ON TANGENT BUNDLE $T(M)$. Konuralp J. Math. October 2016;4(2):209-216.
Chicago Cayır, HASIM. “COVARIENT DERIVATIVES OF ALMOST CONTACT STRUCTURE AND ALMOST PARACONTACT STRUCTURE WITH RESPECT TO $X^{C}$ AND $X^{V}$ ON TANGENT BUNDLE $T(M)$”. Konuralp Journal of Mathematics 4, no. 2 (October 2016): 209-16.
EndNote Cayır H (October 1, 2016) COVARIENT DERIVATIVES OF ALMOST CONTACT STRUCTURE AND ALMOST PARACONTACT STRUCTURE WITH RESPECT TO $X^{C}$ AND $X^{V}$ ON TANGENT BUNDLE $T(M)$. Konuralp Journal of Mathematics 4 2 209–216.
IEEE H. Cayır, “COVARIENT DERIVATIVES OF ALMOST CONTACT STRUCTURE AND ALMOST PARACONTACT STRUCTURE WITH RESPECT TO $X^{C}$ AND $X^{V}$ ON TANGENT BUNDLE $T(M)$”, Konuralp J. Math., vol. 4, no. 2, pp. 209–216, 2016.
ISNAD Cayır, HASIM. “COVARIENT DERIVATIVES OF ALMOST CONTACT STRUCTURE AND ALMOST PARACONTACT STRUCTURE WITH RESPECT TO $X^{C}$ AND $X^{V}$ ON TANGENT BUNDLE $T(M)$”. Konuralp Journal of Mathematics 4/2 (October 2016), 209-216.
JAMA Cayır H. COVARIENT DERIVATIVES OF ALMOST CONTACT STRUCTURE AND ALMOST PARACONTACT STRUCTURE WITH RESPECT TO $X^{C}$ AND $X^{V}$ ON TANGENT BUNDLE $T(M)$. Konuralp J. Math. 2016;4:209–216.
MLA Cayır, HASIM. “COVARIENT DERIVATIVES OF ALMOST CONTACT STRUCTURE AND ALMOST PARACONTACT STRUCTURE WITH RESPECT TO $X^{C}$ AND $X^{V}$ ON TANGENT BUNDLE $T(M)$”. Konuralp Journal of Mathematics, vol. 4, no. 2, 2016, pp. 209-16.
Vancouver Cayır H. COVARIENT DERIVATIVES OF ALMOST CONTACT STRUCTURE AND ALMOST PARACONTACT STRUCTURE WITH RESPECT TO $X^{C}$ AND $X^{V}$ ON TANGENT BUNDLE $T(M)$. Konuralp J. Math. 2016;4(2):209-16.
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