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Year 2016, Volume: 4 Issue: 4, 42 - 50, 31.12.2016

Hasim Cayir , Kubra Akdag

Abstract

References

  • M.A.Akyol, B.S¸ahin, Conformal anti-invariant submersions from almost Hermitian manifolds, Turkish Journal of Mathematics, 40 (2016) 43-70.
  • D.E.Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Math, 509, Springer Verlag, New York, (1976).
  • S.Buyukkutuk, ˙I.Kis¸i, V.N.Mishra, G.¨Ozt¨urk, Some Characterizations of Curves in Galilean 3-Space G3, Facta Universitatis, Series: Mathematics and Informatics, 31 (2) (2016) 503-512.
  • H.C¸ ayır, Some Notes on Lifts of Almost Paracontact Structures, American Review of Mathematics and Statistics, 3 (1) (2015) 52-60.
  • H.C¸ ayır, Lie derivatives of almost contact structure and almost paracontact structure with respect to XV and XH on tangent bundle T(M), Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, 42 (1) (2016) 38-49.
  • H.C¸ ayır, Tachibana and Vishnevskii Operators Applied to XV and XC in Almost Paracontact Structure on Tangent Bundle T(M), Ordu ¨Universitesi Bilim ve Teknoloji Dergisi, Ordu ¨Universitesi, 6 (1) (2016) 67-82.
  • ] H.C¸ ayır, Tachibana and Vishnevskii Operators Applied to XV and XH in Almost Paracontact Structure on Tangent Bundle T(M), New Trends in Mathematical Sciences, 4 (3) (2016) 105-115.
  • H.C¸ ayır, G.K¨oseo˘glu, Lie Derivatives of Almost Contact Structure and Almost Paracontact Structure With Respect to XC and XV on Tangent Bundle T(M). New Trends in Mathematical Sciences, 4 (1) (2016) 153-159.
  • Deepmala, L.N.Mishra, Differential operators over modules and rings as a path to the generalized differential geometry, Facta Universitatis (NIS) Ser. Math. Inform., 30 (5) (2015) 753-764.
  • A.Gezer, L.Bilen, A.C¸ akmak, Properties of Modified Riemannian Extensions, Journal of Mathematical Physics, Analysis, Geometry, 11 (2) (2015) 159-173.
  • Y.Gunduzalp, Neutral slant submanifolds of a para-Kahler manifold, Abstract and Applied Analysis, (2013), Doi:10.1155/2013/752650, pp.1-8.
  • S. Kaneyuki, F.L.Williams, Almost Para-Contact and Para-Hodge Structures on Manifolds, Nagoya Math. J., 99 (1985) 173-187.
  • S.Kızıltu˘g, S.Yurttanc¸ıkmaz, A.C¸ akmak, Normal and Rectifying Curves in the Equiform Differential Geometry of G3, Poincare Journal of Analysis & Applications, 2 (2014), 55 – 61.
  • I.Kis¸i, S.B¨uy¨ukk¨ut¨uk, Deepmala, G.¨Ozt¨urk, AW(k)-type Curves According to Parallel Transport Frame in Euclidean Space E4, Facta Universitatis (NIS) Ser. Math. Inform., 31 (4) (2016).
  • P.Libermann, Sur les Structures Presque Para-Complexes, C.R. Acad. Sci. Paris Ser. I Math., 234 (1952) 2517-2519.
  • S.Das, Lovejoy, Fiberings on almost r-contact manifolds, Publicationes Mathematicae, Debrecen, Hungary 43 (1993) 161-167.
  • V.N.Mishra, Some Problems on Approximations of Functions in Banach Spaces, Ph.D.Thesis, Indian Institue of Technology, Roorkee 247 667, Uttarakhand, India (2007).
  • V.N.Mishra, K.Khatri, L.N.Mishra, Deepmala, Inverse result in simultaneous approximation by Baskakov-Durrmeyer-Stancu operators, Journal of Inequalites and Applications, 586 (2013), doi:10.1186/1029-242X-2013-586.
  • F.Ocak, A.A.Salimov, Geometry of the cotangent bundle with Sasakian metricsand its applications, Proc. Indian Acad. Sci. (Math. Sci.), 124 (3) (August 2014) 427–436.
  • V.Oproiu, Some remarkable structures and connexions, defined on the tangent bundle, Rendiconti di Matematica 3 (1973) 6 VI.
  • T.Omran, A.Sharffuddin, S.I.Husain, Lift of Structures on Manifolds, Publications de 1’Instıtut Mathematıqe, Nouvelle serie, 360 (50) (1984) 93 – 97.
  • A.A.Salimov, Tensor Operators and Their applications, Nova Science Publ., New York (2013).
  • A.A.Salimov, H.C¸ ayır, Some Notes On Almost Paracontact Structures, Comptes Rendus de 1’Acedemie Bulgare Des Sciences,66 (3) (2013) 331-338.
  • S.Sasaki, On The Differantial Geometry of Tangent Boundles of Riemannian Manifolds, Tohoku Math. J., no.10(1958) 338-358.
  • B.S¸ahin, M.A.Akyol, Golden maps betwen Golden Riemannian manifolds and constancy of certain maps, Math. Commun., 19(2014) 333-342.
  • Vandana, Deepmala, K.Drachal, V.N.Mishra, Some algebro-geometric aspects of spacetime c-boundary, Mathematica Aeterna, accepted on July 28, in press.
  • K.Yano, S.Ishihara, Tangent and Cotangent Bundles, Marcel Dekker Inc, New York (1973).

Some notes on almost paracomplex structures associated with the diagonal lifts and operators on cotangent bundle T*(M^n)

Year 2016, Volume: 4 Issue: 4, 42 - 50, 31.12.2016

Hasim Cayir , Kubra Akdag

Abstract

In this paper firstly, the Tachibana operators were applied to 1−form, vertical, complete and horizontal lifts with respect to almost paracomplex structure I^D (The diagonal lift I^D ) on cotangent bundle. Secondly, the Vishnevskii operators were applied to 1−form according to the diagonal lift I^D on cotangent bundle. Finally, covariant derivatives of almost paracomplex structure I^D with respect to vertical, complete and horizontal lifts were obtained.

Keywords

Tachibana Operators Vishnevskii Operators Almost Paracomplex Structure Vertical Lift Horizontal Lift

References

  • M.A.Akyol, B.S¸ahin, Conformal anti-invariant submersions from almost Hermitian manifolds, Turkish Journal of Mathematics, 40 (2016) 43-70.
  • D.E.Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Math, 509, Springer Verlag, New York, (1976).
  • S.Buyukkutuk, ˙I.Kis¸i, V.N.Mishra, G.¨Ozt¨urk, Some Characterizations of Curves in Galilean 3-Space G3, Facta Universitatis, Series: Mathematics and Informatics, 31 (2) (2016) 503-512.
  • H.C¸ ayır, Some Notes on Lifts of Almost Paracontact Structures, American Review of Mathematics and Statistics, 3 (1) (2015) 52-60.
  • H.C¸ ayır, Lie derivatives of almost contact structure and almost paracontact structure with respect to XV and XH on tangent bundle T(M), Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, 42 (1) (2016) 38-49.
  • H.C¸ ayır, Tachibana and Vishnevskii Operators Applied to XV and XC in Almost Paracontact Structure on Tangent Bundle T(M), Ordu ¨Universitesi Bilim ve Teknoloji Dergisi, Ordu ¨Universitesi, 6 (1) (2016) 67-82.
  • ] H.C¸ ayır, Tachibana and Vishnevskii Operators Applied to XV and XH in Almost Paracontact Structure on Tangent Bundle T(M), New Trends in Mathematical Sciences, 4 (3) (2016) 105-115.
  • H.C¸ ayır, G.K¨oseo˘glu, Lie Derivatives of Almost Contact Structure and Almost Paracontact Structure With Respect to XC and XV on Tangent Bundle T(M). New Trends in Mathematical Sciences, 4 (1) (2016) 153-159.
  • Deepmala, L.N.Mishra, Differential operators over modules and rings as a path to the generalized differential geometry, Facta Universitatis (NIS) Ser. Math. Inform., 30 (5) (2015) 753-764.
  • A.Gezer, L.Bilen, A.C¸ akmak, Properties of Modified Riemannian Extensions, Journal of Mathematical Physics, Analysis, Geometry, 11 (2) (2015) 159-173.
  • Y.Gunduzalp, Neutral slant submanifolds of a para-Kahler manifold, Abstract and Applied Analysis, (2013), Doi:10.1155/2013/752650, pp.1-8.
  • S. Kaneyuki, F.L.Williams, Almost Para-Contact and Para-Hodge Structures on Manifolds, Nagoya Math. J., 99 (1985) 173-187.
  • S.Kızıltu˘g, S.Yurttanc¸ıkmaz, A.C¸ akmak, Normal and Rectifying Curves in the Equiform Differential Geometry of G3, Poincare Journal of Analysis & Applications, 2 (2014), 55 – 61.
  • I.Kis¸i, S.B¨uy¨ukk¨ut¨uk, Deepmala, G.¨Ozt¨urk, AW(k)-type Curves According to Parallel Transport Frame in Euclidean Space E4, Facta Universitatis (NIS) Ser. Math. Inform., 31 (4) (2016).
  • P.Libermann, Sur les Structures Presque Para-Complexes, C.R. Acad. Sci. Paris Ser. I Math., 234 (1952) 2517-2519.
  • S.Das, Lovejoy, Fiberings on almost r-contact manifolds, Publicationes Mathematicae, Debrecen, Hungary 43 (1993) 161-167.
  • V.N.Mishra, Some Problems on Approximations of Functions in Banach Spaces, Ph.D.Thesis, Indian Institue of Technology, Roorkee 247 667, Uttarakhand, India (2007).
  • V.N.Mishra, K.Khatri, L.N.Mishra, Deepmala, Inverse result in simultaneous approximation by Baskakov-Durrmeyer-Stancu operators, Journal of Inequalites and Applications, 586 (2013), doi:10.1186/1029-242X-2013-586.
  • F.Ocak, A.A.Salimov, Geometry of the cotangent bundle with Sasakian metricsand its applications, Proc. Indian Acad. Sci. (Math. Sci.), 124 (3) (August 2014) 427–436.
  • V.Oproiu, Some remarkable structures and connexions, defined on the tangent bundle, Rendiconti di Matematica 3 (1973) 6 VI.
  • T.Omran, A.Sharffuddin, S.I.Husain, Lift of Structures on Manifolds, Publications de 1’Instıtut Mathematıqe, Nouvelle serie, 360 (50) (1984) 93 – 97.
  • A.A.Salimov, Tensor Operators and Their applications, Nova Science Publ., New York (2013).
  • A.A.Salimov, H.C¸ ayır, Some Notes On Almost Paracontact Structures, Comptes Rendus de 1’Acedemie Bulgare Des Sciences,66 (3) (2013) 331-338.
  • S.Sasaki, On The Differantial Geometry of Tangent Boundles of Riemannian Manifolds, Tohoku Math. J., no.10(1958) 338-358.
  • B.S¸ahin, M.A.Akyol, Golden maps betwen Golden Riemannian manifolds and constancy of certain maps, Math. Commun., 19(2014) 333-342.
  • Vandana, Deepmala, K.Drachal, V.N.Mishra, Some algebro-geometric aspects of spacetime c-boundary, Mathematica Aeterna, accepted on July 28, in press.
  • K.Yano, S.Ishihara, Tangent and Cotangent Bundles, Marcel Dekker Inc, New York (1973).
There are 27 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Hasim Cayir

Kubra Akdag This is me

Publication Date December 31, 2016
Published in Issue Year 2016 Volume: 4 Issue: 4

Cite

APA Cayir, H., & Akdag, K. (2016). Some notes on almost paracomplex structures associated with the diagonal lifts and operators on cotangent bundle T*(M^n). New Trends in Mathematical Sciences, 4(4), 42-50.
AMA Cayir H, Akdag K. Some notes on almost paracomplex structures associated with the diagonal lifts and operators on cotangent bundle T*(M^n). New Trends in Mathematical Sciences. December 2016;4(4):42-50.
Chicago Cayir, Hasim, and Kubra Akdag. “Some Notes on Almost Paracomplex Structures Associated With the Diagonal Lifts and Operators on Cotangent Bundle T*(M^n)”. New Trends in Mathematical Sciences 4, no. 4 (December 2016): 42-50.
EndNote Cayir H, Akdag K (December 1, 2016) Some notes on almost paracomplex structures associated with the diagonal lifts and operators on cotangent bundle T*(M^n). New Trends in Mathematical Sciences 4 4 42–50.
IEEE H. Cayir and K. Akdag, “Some notes on almost paracomplex structures associated with the diagonal lifts and operators on cotangent bundle T*(M^n)”, New Trends in Mathematical Sciences, vol. 4, no. 4, pp. 42–50, 2016.
ISNAD Cayir, Hasim - Akdag, Kubra. “Some Notes on Almost Paracomplex Structures Associated With the Diagonal Lifts and Operators on Cotangent Bundle T*(M^n)”. New Trends in Mathematical Sciences 4/4 (December 2016), 42-50.
JAMA Cayir H, Akdag K. Some notes on almost paracomplex structures associated with the diagonal lifts and operators on cotangent bundle T*(M^n). New Trends in Mathematical Sciences. 2016;4:42–50.
MLA Cayir, Hasim and Kubra Akdag. “Some Notes on Almost Paracomplex Structures Associated With the Diagonal Lifts and Operators on Cotangent Bundle T*(M^n)”. New Trends in Mathematical Sciences, vol. 4, no. 4, 2016, pp. 42-50.
Vancouver Cayir H, Akdag K. Some notes on almost paracomplex structures associated with the diagonal lifts and operators on cotangent bundle T*(M^n). New Trends in Mathematical Sciences. 2016;4(4):42-50.