Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2019, Cilt: 32 Sayı: 1, 242 - 254, 01.03.2019

Öz

Kaynakça

  • \bibitem{AAAS} A. Akbar and A. Sarkar,\,\,\emph{Some Curvature Properties of Trans-Sasakian Manifolds,}\,\, Lobachevskii Journal of Mathematics, 35(2), 2014, 56-64.
  • \bibitem{BBAKR} B. Barua and A.K. Ray,\,\ \emph{Some properties of semi-symmetric metric connetion in a Riemannian manifold,} Indian J. Pure Appl. Math., 16(7), (1985), 726-740.
  • \bibitem{icts} D.E. Blair,\,\ \emph{Contact manifolds in Riemannian geometry,% } Lecture Notes in Mathematics, 509 Springer-Verlag, Berlin, 1976.
  • \bibitem{SDMMT} S. Deshmukh and M.M. Tripathi,\,\,\emph{A note on trans-Sasakian manifolds,}\,\, Math. Slov. 63(6), (2013), 1361-1370.
  • \bibitem{UCDeASarkar} U. C. De and A. Sarkar,\,\ \emph{On Three-Dimensional Trans-Sasakian Manifolds,} Extracta mathematicae, 23(3), 2008, 265-277.
  • \bibitem{UCDMMT} U.C. De and M.M. Tripathi,\,\,\emph{Ricci tensor in 3-dimensional trans-Sasakian manifolds,}\,\, Kyungpook Math. J., 43(2), (2003), 247-255.
  • \bibitem{UCDKD} U.C. De and K. De,\,\,\emph{On a class of three-dimensional Trans-Sasakian manifolds,}\,\, Commun. Korean Math. Soc. 27(4), (2012), 795-808.
  • \bibitem{UCDAB} U.C. De and A. Barman,\,\ \emph{On a type of semisymmetric metric connection on a Riemannian manifold,} Publications De L'institut Math% \'{e}matique Nouvelle s\'{e}rie, tome, 98(112), (2015), 211-218.
  • \bibitem{GrayAHervellaLM} A. Gray, L.M. Hervella,\,\,\emph{The sixteen classes of almost Hermitian manifolds and their linear invariants,} \,\, Ann. Mat. Pura Appl., 123(4), 1980, 35-58.
  • \bibitem{HAHayden} H.A. Hayden.\,\,{\ Subspaces of a space with torsion.}% \,\, Proc. London Math. Soc., 34, 1932, 27-50.
  • \bibitem{KKenmotsu} K. Kenmotsu,\,\,\emph{A class of almost contact Riemannian manifolds,}\,\, T\^{o}hoku Math. J., 24, (1972), 93-103.
  • \bibitem{KHDDAB} Kalyan Halder, Dipankar Debnath and Arindam Bhattacharyya,\,\ \emph{Semi-Symmetric Metric Connection on a 3-Dimensional Trans-Sasakian Manifold,} International J.Math. Combin., 3, (2013), 16-21.
  • \bibitem{JSKRPMMT} J.S. Kim, R. Prasad and M.M. Tripathi,\,\,\emph{On generalized Ricci-recurrent trans-Sasakian manifolds,}\,\, J. Korean Math. Soc., 39(6), (2002), 953-961.
  • \bibitem{VFK} V.F. Kirichenko,\,\,\emph{On the geometry of nearly trans-Sasakian manifolds,}\,\, Dokl Akad. Nauk 397(6), (2004), 733-736.
  • \bibitem{MarreroJC} J.C. Marrero,\thinspace \thinspace \emph{The local structure of trans-Sasakian manifolds,}\thinspace \thinspace\ Ann. Mat. Pure Appl., 162, 1992, 77-86.
  • %\bibitem{HGN} H.G. Nagaraja,\,\,{\em $\phi$-recurrent Trans-Sasakian manifolds,}\,\, Matematiqki Vesnik, 63(2), (2011), 79-86.
  • \bibitem{OubinaJA} J.A. Oubina,\,\,\emph{New classes of almost contact metric structures,}\,\, Publ. Math. Debr., 32(3--4), 1985, 187-193.
  • \bibitem{DGPCSBV} D.G. Prakasha, C.S. Bagewadi and Venkatesha,\,\,\emph{% Conformally and quasi-conformally conservative curvature tensors on a trans-Sasakian manifold with respect to semi-symmetric metric connections,}% \,\, Diff. Geometry-Dyn.Sys., 10, (2008), 263-274.
  • \bibitem{CSBDGPV} D.G. Prakasha, C.S. Bagewadi and Venkatesha,\,\,\emph{% Conservative Projective Curvature Tensor On Trans-sasakian Manifolds With Respect To Semi-symmetric Metric Connection,}\,\, An. S% %TCIMACRO{\U{b8}}% %BeginExpansion \c{}% %EndExpansion t. Univ. Ovidius Constanta, 15(2), 2007, 5-18.
  • \bibitem{ASPAB} A. Sampa Pahan and Arindam Bhattacharyya,\,\ \emph{Some Properties of Three Dimensional Trans-Sasakian Manifolds with a Semi-Symmetric Metric Connection,} Lobachevskii Journal of Mathematics, 37(2), 2016, 177-184.
  • \bibitem{AASKKBSE} A.A. Shaikh, K.K. Baishya and S. Eyasmin,\,\,\emph{On $D$% -homothetic deformation of trans-Sasakian structure,}\,\, Demonstratio Mathematica, 41(1), 2008, 171-188.
  • \bibitem{ASSKHMS} A. Sarkar, S.K. Hui and Matilal Sen,\,\,\emph{A Study on Legendre Curves in 3-Dimensional Trans-Sasakian Manifolds,}\,\, Lobachevskii Journal of Mathematics, 35(1), 2014, 11-18.
  • \bibitem{AASSKH} A.A. Shaikh and S.K. Hui,\,\,\emph{On weak symmetries of trans-Sasakian manifolds,}\,\, Proceedings of the Estonian Academy of Sciences, 58(4), 2009, 213-223.
  • \bibitem{tvs10} A. Turgut Vanli and R. Sari,\,\,\emph{ Invariant submanifolds of trans-Sasakian manifolds,}\,\, Differ. Geom. Dyn. Syst. 12, 2010, 277-288.
  • \bibitem{tvs11} A. Turgut Vanli and R. Sari,\,\,\emph{On invariant submanifolds of a nearly trans-Sasakian manifold,}\,\, \,\, Arab. J. Sci. Eng. 36 (3) 2011, 423-429.
  • \bibitem{KYano1} K. Yano,\thinspace \thinspace \emph{Concircular geometry I. Concircular transformations,}\thinspace \thinspace\ Proc. Imp. Acad. Tokyo 16, (1940), 195-200.
  • \bibitem{KYano2} K. Yano,\,\,\emph{On semi-symmetric metric connections.}% \,\, Rev. Roumaine Math. Pures Appl., 15, 1970, 1579-1586.

On 3-dimensional Trans-Sasakian manifold admitting a semi symmetric metric connection

Yıl 2019, Cilt: 32 Sayı: 1, 242 - 254, 01.03.2019

Öz

The
purpose of the present paper is to study 
3-dimensional trans-Sasakian manifold admitting a semi-symmetric metric
connection. Here we mainly study locally




















-symmetric and locally

-concircularly symmetric 3-dimensional trans-Sasakian
manifold admitting a semi-symmetric metric connection. Moreover, we examine our
results and the results of [1] and [2] by constructing some examples. 

Kaynakça

  • \bibitem{AAAS} A. Akbar and A. Sarkar,\,\,\emph{Some Curvature Properties of Trans-Sasakian Manifolds,}\,\, Lobachevskii Journal of Mathematics, 35(2), 2014, 56-64.
  • \bibitem{BBAKR} B. Barua and A.K. Ray,\,\ \emph{Some properties of semi-symmetric metric connetion in a Riemannian manifold,} Indian J. Pure Appl. Math., 16(7), (1985), 726-740.
  • \bibitem{icts} D.E. Blair,\,\ \emph{Contact manifolds in Riemannian geometry,% } Lecture Notes in Mathematics, 509 Springer-Verlag, Berlin, 1976.
  • \bibitem{SDMMT} S. Deshmukh and M.M. Tripathi,\,\,\emph{A note on trans-Sasakian manifolds,}\,\, Math. Slov. 63(6), (2013), 1361-1370.
  • \bibitem{UCDeASarkar} U. C. De and A. Sarkar,\,\ \emph{On Three-Dimensional Trans-Sasakian Manifolds,} Extracta mathematicae, 23(3), 2008, 265-277.
  • \bibitem{UCDMMT} U.C. De and M.M. Tripathi,\,\,\emph{Ricci tensor in 3-dimensional trans-Sasakian manifolds,}\,\, Kyungpook Math. J., 43(2), (2003), 247-255.
  • \bibitem{UCDKD} U.C. De and K. De,\,\,\emph{On a class of three-dimensional Trans-Sasakian manifolds,}\,\, Commun. Korean Math. Soc. 27(4), (2012), 795-808.
  • \bibitem{UCDAB} U.C. De and A. Barman,\,\ \emph{On a type of semisymmetric metric connection on a Riemannian manifold,} Publications De L'institut Math% \'{e}matique Nouvelle s\'{e}rie, tome, 98(112), (2015), 211-218.
  • \bibitem{GrayAHervellaLM} A. Gray, L.M. Hervella,\,\,\emph{The sixteen classes of almost Hermitian manifolds and their linear invariants,} \,\, Ann. Mat. Pura Appl., 123(4), 1980, 35-58.
  • \bibitem{HAHayden} H.A. Hayden.\,\,{\ Subspaces of a space with torsion.}% \,\, Proc. London Math. Soc., 34, 1932, 27-50.
  • \bibitem{KKenmotsu} K. Kenmotsu,\,\,\emph{A class of almost contact Riemannian manifolds,}\,\, T\^{o}hoku Math. J., 24, (1972), 93-103.
  • \bibitem{KHDDAB} Kalyan Halder, Dipankar Debnath and Arindam Bhattacharyya,\,\ \emph{Semi-Symmetric Metric Connection on a 3-Dimensional Trans-Sasakian Manifold,} International J.Math. Combin., 3, (2013), 16-21.
  • \bibitem{JSKRPMMT} J.S. Kim, R. Prasad and M.M. Tripathi,\,\,\emph{On generalized Ricci-recurrent trans-Sasakian manifolds,}\,\, J. Korean Math. Soc., 39(6), (2002), 953-961.
  • \bibitem{VFK} V.F. Kirichenko,\,\,\emph{On the geometry of nearly trans-Sasakian manifolds,}\,\, Dokl Akad. Nauk 397(6), (2004), 733-736.
  • \bibitem{MarreroJC} J.C. Marrero,\thinspace \thinspace \emph{The local structure of trans-Sasakian manifolds,}\thinspace \thinspace\ Ann. Mat. Pure Appl., 162, 1992, 77-86.
  • %\bibitem{HGN} H.G. Nagaraja,\,\,{\em $\phi$-recurrent Trans-Sasakian manifolds,}\,\, Matematiqki Vesnik, 63(2), (2011), 79-86.
  • \bibitem{OubinaJA} J.A. Oubina,\,\,\emph{New classes of almost contact metric structures,}\,\, Publ. Math. Debr., 32(3--4), 1985, 187-193.
  • \bibitem{DGPCSBV} D.G. Prakasha, C.S. Bagewadi and Venkatesha,\,\,\emph{% Conformally and quasi-conformally conservative curvature tensors on a trans-Sasakian manifold with respect to semi-symmetric metric connections,}% \,\, Diff. Geometry-Dyn.Sys., 10, (2008), 263-274.
  • \bibitem{CSBDGPV} D.G. Prakasha, C.S. Bagewadi and Venkatesha,\,\,\emph{% Conservative Projective Curvature Tensor On Trans-sasakian Manifolds With Respect To Semi-symmetric Metric Connection,}\,\, An. S% %TCIMACRO{\U{b8}}% %BeginExpansion \c{}% %EndExpansion t. Univ. Ovidius Constanta, 15(2), 2007, 5-18.
  • \bibitem{ASPAB} A. Sampa Pahan and Arindam Bhattacharyya,\,\ \emph{Some Properties of Three Dimensional Trans-Sasakian Manifolds with a Semi-Symmetric Metric Connection,} Lobachevskii Journal of Mathematics, 37(2), 2016, 177-184.
  • \bibitem{AASKKBSE} A.A. Shaikh, K.K. Baishya and S. Eyasmin,\,\,\emph{On $D$% -homothetic deformation of trans-Sasakian structure,}\,\, Demonstratio Mathematica, 41(1), 2008, 171-188.
  • \bibitem{ASSKHMS} A. Sarkar, S.K. Hui and Matilal Sen,\,\,\emph{A Study on Legendre Curves in 3-Dimensional Trans-Sasakian Manifolds,}\,\, Lobachevskii Journal of Mathematics, 35(1), 2014, 11-18.
  • \bibitem{AASSKH} A.A. Shaikh and S.K. Hui,\,\,\emph{On weak symmetries of trans-Sasakian manifolds,}\,\, Proceedings of the Estonian Academy of Sciences, 58(4), 2009, 213-223.
  • \bibitem{tvs10} A. Turgut Vanli and R. Sari,\,\,\emph{ Invariant submanifolds of trans-Sasakian manifolds,}\,\, Differ. Geom. Dyn. Syst. 12, 2010, 277-288.
  • \bibitem{tvs11} A. Turgut Vanli and R. Sari,\,\,\emph{On invariant submanifolds of a nearly trans-Sasakian manifold,}\,\, \,\, Arab. J. Sci. Eng. 36 (3) 2011, 423-429.
  • \bibitem{KYano1} K. Yano,\thinspace \thinspace \emph{Concircular geometry I. Concircular transformations,}\thinspace \thinspace\ Proc. Imp. Acad. Tokyo 16, (1940), 195-200.
  • \bibitem{KYano2} K. Yano,\,\,\emph{On semi-symmetric metric connections.}% \,\, Rev. Roumaine Math. Pures Appl., 15, 1970, 1579-1586.
Toplam 27 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Mathematics
Yazarlar

Srivaishnava Vasudeva Vıshnuvardhana

Venkatesh Venkatesha

Aysel Turgut Vanlı

Yayımlanma Tarihi 1 Mart 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 32 Sayı: 1

Kaynak Göster

APA Vıshnuvardhana, S. V., Venkatesha, V., & Turgut Vanlı, A. (2019). On 3-dimensional Trans-Sasakian manifold admitting a semi symmetric metric connection. Gazi University Journal of Science, 32(1), 242-254.
AMA Vıshnuvardhana SV, Venkatesha V, Turgut Vanlı A. On 3-dimensional Trans-Sasakian manifold admitting a semi symmetric metric connection. Gazi University Journal of Science. Mart 2019;32(1):242-254.
Chicago Vıshnuvardhana, Srivaishnava Vasudeva, Venkatesh Venkatesha, ve Aysel Turgut Vanlı. “On 3-Dimensional Trans-Sasakian Manifold Admitting a Semi Symmetric Metric Connection”. Gazi University Journal of Science 32, sy. 1 (Mart 2019): 242-54.
EndNote Vıshnuvardhana SV, Venkatesha V, Turgut Vanlı A (01 Mart 2019) On 3-dimensional Trans-Sasakian manifold admitting a semi symmetric metric connection. Gazi University Journal of Science 32 1 242–254.
IEEE S. V. Vıshnuvardhana, V. Venkatesha, ve A. Turgut Vanlı, “On 3-dimensional Trans-Sasakian manifold admitting a semi symmetric metric connection”, Gazi University Journal of Science, c. 32, sy. 1, ss. 242–254, 2019.
ISNAD Vıshnuvardhana, Srivaishnava Vasudeva vd. “On 3-Dimensional Trans-Sasakian Manifold Admitting a Semi Symmetric Metric Connection”. Gazi University Journal of Science 32/1 (Mart 2019), 242-254.
JAMA Vıshnuvardhana SV, Venkatesha V, Turgut Vanlı A. On 3-dimensional Trans-Sasakian manifold admitting a semi symmetric metric connection. Gazi University Journal of Science. 2019;32:242–254.
MLA Vıshnuvardhana, Srivaishnava Vasudeva vd. “On 3-Dimensional Trans-Sasakian Manifold Admitting a Semi Symmetric Metric Connection”. Gazi University Journal of Science, c. 32, sy. 1, 2019, ss. 242-54.
Vancouver Vıshnuvardhana SV, Venkatesha V, Turgut Vanlı A. On 3-dimensional Trans-Sasakian manifold admitting a semi symmetric metric connection. Gazi University Journal of Science. 2019;32(1):242-54.