Research Article
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A new connection in a Riemannian manifold

Year 2008, Volume 1, Issue 1, 15 - 24, 30.04.2008

Abstract

In a Riemannian manifold, the existence of a new connection is
proved. In particular cases, this connection reduces to several symmetric,
semi-symmetric and quarter-symmetric connections; even some of them are
not introduced so far. We also found formula for curvature tensor of this new
connection.

References

  • [1] Agashe, N. S. and Chafle, M. R., A semi-symmetric non-metric connection in a Riemannian manifold, Indian J. Pure Appl. Math., 23(1992), 399-409.
  • [2] Andonie, O. C. and Smaranda, D., Certaines connexions semi-symmetriques, Tensor (N.S.),31(1977), 8-12.
  • [3] Eisenhart, L. P., Continuous groups of transformations, Dover Publications, Inc., New York, 1961.
  • [4] Friedmann, A. and Schouten, J. A., Über die geometrie der halbsymmetrischen Äubertragung, Math. Zeitschr. 21(1924), 211-223.
  • [5] Folland, G. B., Weyl manifolds, J. Dif. Geometry, 4(1970), 145-153.
  • [6] Golab, S., On semi-symmetric and quarter-symmetric linear connections, Tensor (N.S.), 29(1975), 249-254.
  • [7] Hayden, H. A., Subspaces of a space with torsion, Proc. London Math. Soc., 34(1932), 27-50.
  • [8] Liang, Y., On semi-symmetric recurrent-metric connection, Tensor (N.S.), 55(1994), 107-112.
  • [9] Mishra, R. S. and Pandey, S. N., On quarter-symmetric metric F-connections, Tensor (N.S.), 34(1980), 1-7. [10] Ojha, R. H. and Prasad, S., Semi-symmetric metric s-connection in a Sasakian manifold, Indian J. Pure Appl. Math., 16(1985), no. 4, 341-344.
  • [11] Pak, E., On the pseudo-Riemannian spaces, J. Korean Math. Soc., 6(1969), 23-31.
  • [12] Rastogi, S. C., On quarter-symmetric metric connection, C. R. Acad. Bulg. Sci., 31(1978), no. 8, 811-814.
  • [13] Rastogi, S. C., On quarter-symmetric metric connections, Tensor (N.S.), 44(1987), 133-141.
  • [14] Schmidt, B. G., Conditions on a connection to be a metric connection, Commun. Math. Phys., 29(1973), 55-59.
  • [15] Schouten, J. A., Ricci calculus, Springer, 1954.
  • [16] Sengupta, J. , De, U. C. and Binh, T. Q., On a type of semi-symmetric non-metric connection on a Riemannian manifold, Indian J. Pure Appl. Math., 31(2000), no. 12, 1659-1670.
  • [17] Smaranda, D., On projective transformations of symmetric connections with a recurrent projective tensor field, Proc. Nat.Coll. on Geometry and Topology (Busteni, 1981), 323-329, Univ. Bucaresti, Bucharest, 1983.
  • [18] Tamassy, L. and Binh, T. Q., On the non-existence of certain connections with torsion and of constant curvature, Publ. Math. Debrecen, 36(1989), 283-288.
  • [19] Yano, K., Integral formulas in Riemannian geometry, Marcel Dekker Inc., 1970.
  • [20] Yano, K., On semi-symmetric metric connections, Rev. Roumaine Math. Pures Appl. 15(1970), 1579-1586.
  • [21] Yano, K. and Imai, T., On semi-symmetric metric Á-connections in a Sasakian manifold, Kodai Math. Sem. Rep. 28(1977), 150-158.
  • [22] Yano, K. and Imai, T., Quarter-symmetric metric connections and their curvature tensors, Tensor (N.S.), 38(1982), 13-18.

Year 2008, Volume 1, Issue 1, 15 - 24, 30.04.2008

Abstract

References

  • [1] Agashe, N. S. and Chafle, M. R., A semi-symmetric non-metric connection in a Riemannian manifold, Indian J. Pure Appl. Math., 23(1992), 399-409.
  • [2] Andonie, O. C. and Smaranda, D., Certaines connexions semi-symmetriques, Tensor (N.S.),31(1977), 8-12.
  • [3] Eisenhart, L. P., Continuous groups of transformations, Dover Publications, Inc., New York, 1961.
  • [4] Friedmann, A. and Schouten, J. A., Über die geometrie der halbsymmetrischen Äubertragung, Math. Zeitschr. 21(1924), 211-223.
  • [5] Folland, G. B., Weyl manifolds, J. Dif. Geometry, 4(1970), 145-153.
  • [6] Golab, S., On semi-symmetric and quarter-symmetric linear connections, Tensor (N.S.), 29(1975), 249-254.
  • [7] Hayden, H. A., Subspaces of a space with torsion, Proc. London Math. Soc., 34(1932), 27-50.
  • [8] Liang, Y., On semi-symmetric recurrent-metric connection, Tensor (N.S.), 55(1994), 107-112.
  • [9] Mishra, R. S. and Pandey, S. N., On quarter-symmetric metric F-connections, Tensor (N.S.), 34(1980), 1-7. [10] Ojha, R. H. and Prasad, S., Semi-symmetric metric s-connection in a Sasakian manifold, Indian J. Pure Appl. Math., 16(1985), no. 4, 341-344.
  • [11] Pak, E., On the pseudo-Riemannian spaces, J. Korean Math. Soc., 6(1969), 23-31.
  • [12] Rastogi, S. C., On quarter-symmetric metric connection, C. R. Acad. Bulg. Sci., 31(1978), no. 8, 811-814.
  • [13] Rastogi, S. C., On quarter-symmetric metric connections, Tensor (N.S.), 44(1987), 133-141.
  • [14] Schmidt, B. G., Conditions on a connection to be a metric connection, Commun. Math. Phys., 29(1973), 55-59.
  • [15] Schouten, J. A., Ricci calculus, Springer, 1954.
  • [16] Sengupta, J. , De, U. C. and Binh, T. Q., On a type of semi-symmetric non-metric connection on a Riemannian manifold, Indian J. Pure Appl. Math., 31(2000), no. 12, 1659-1670.
  • [17] Smaranda, D., On projective transformations of symmetric connections with a recurrent projective tensor field, Proc. Nat.Coll. on Geometry and Topology (Busteni, 1981), 323-329, Univ. Bucaresti, Bucharest, 1983.
  • [18] Tamassy, L. and Binh, T. Q., On the non-existence of certain connections with torsion and of constant curvature, Publ. Math. Debrecen, 36(1989), 283-288.
  • [19] Yano, K., Integral formulas in Riemannian geometry, Marcel Dekker Inc., 1970.
  • [20] Yano, K., On semi-symmetric metric connections, Rev. Roumaine Math. Pures Appl. 15(1970), 1579-1586.
  • [21] Yano, K. and Imai, T., On semi-symmetric metric Á-connections in a Sasakian manifold, Kodai Math. Sem. Rep. 28(1977), 150-158.
  • [22] Yano, K. and Imai, T., Quarter-symmetric metric connections and their curvature tensors, Tensor (N.S.), 38(1982), 13-18.

Details

Primary Language English
Journal Section Research Article
Authors

Mukut MANİ TRİPATHİ>

Publication Date April 30, 2008
Published in Issue Year 2008, Volume 1, Issue 1

Cite

Bibtex @research article { iejg581485, journal = {International Electronic Journal of Geometry}, eissn = {1307-5624}, address = {}, publisher = {Kazım İLARSLAN}, year = {2008}, volume = {1}, number = {1}, pages = {15 - 24}, title = {A new connection in a Riemannian manifold}, key = {cite}, author = {Mani Tripathi, Mukut} }
APA Mani Tripathi, M. (2008). A new connection in a Riemannian manifold . International Electronic Journal of Geometry , 1 (1) , 15-24 . Retrieved from https://dergipark.org.tr/en/pub/iejg/issue/46277/581485
MLA Mani Tripathi, M. "A new connection in a Riemannian manifold" . International Electronic Journal of Geometry 1 (2008 ): 15-24 <https://dergipark.org.tr/en/pub/iejg/issue/46277/581485>
Chicago Mani Tripathi, M. "A new connection in a Riemannian manifold". International Electronic Journal of Geometry 1 (2008 ): 15-24
RIS TY - JOUR T1 - A new connection in a Riemannian manifold AU - MukutMani Tripathi Y1 - 2008 PY - 2008 N1 - DO - T2 - International Electronic Journal of Geometry JF - Journal JO - JOR SP - 15 EP - 24 VL - 1 IS - 1 SN - -1307-5624 M3 - UR - Y2 - 2022 ER -
EndNote %0 International Electronic Journal of Geometry A new connection in a Riemannian manifold %A Mukut Mani Tripathi %T A new connection in a Riemannian manifold %D 2008 %J International Electronic Journal of Geometry %P -1307-5624 %V 1 %N 1 %R %U
ISNAD Mani Tripathi, Mukut . "A new connection in a Riemannian manifold". International Electronic Journal of Geometry 1 / 1 (April 2008): 15-24 .
AMA Mani Tripathi M. A new connection in a Riemannian manifold. Int. Electron. J. Geom.. 2008; 1(1): 15-24.
Vancouver Mani Tripathi M. A new connection in a Riemannian manifold. International Electronic Journal of Geometry. 2008; 1(1): 15-24.
IEEE M. Mani Tripathi , "A new connection in a Riemannian manifold", International Electronic Journal of Geometry, vol. 1, no. 1, pp. 15-24, Apr. 2008