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Year 2019, Volume: 32 Issue: 1, 242 - 254, 01.03.2019

Abstract

References

  • \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

Year 2019, Volume: 32 Issue: 1, 242 - 254, 01.03.2019

Abstract

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. 

References

  • \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.
There are 27 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Mathematics
Authors

Srivaishnava Vasudeva Vıshnuvardhana

Venkatesh Venkatesha

Aysel Turgut Vanlı

Publication Date March 1, 2019
Published in Issue Year 2019 Volume: 32 Issue: 1

Cite

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. March 2019;32(1):242-254.
Chicago Vıshnuvardhana, Srivaishnava Vasudeva, Venkatesh Venkatesha, and Aysel Turgut Vanlı. “On 3-Dimensional Trans-Sasakian Manifold Admitting a Semi Symmetric Metric Connection”. Gazi University Journal of Science 32, no. 1 (March 2019): 242-54.
EndNote Vıshnuvardhana SV, Venkatesha V, Turgut Vanlı A (March 1, 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, and A. Turgut Vanlı, “On 3-dimensional Trans-Sasakian manifold admitting a semi symmetric metric connection”, Gazi University Journal of Science, vol. 32, no. 1, pp. 242–254, 2019.
ISNAD Vıshnuvardhana, Srivaishnava Vasudeva et al. “On 3-Dimensional Trans-Sasakian Manifold Admitting a Semi Symmetric Metric Connection”. Gazi University Journal of Science 32/1 (March 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 et al. “On 3-Dimensional Trans-Sasakian Manifold Admitting a Semi Symmetric Metric Connection”. Gazi University Journal of Science, vol. 32, no. 1, 2019, pp. 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.